The Quantized Atomic Masses of the Elements: Part-5; Z=81-99 (Tl-Es)

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European Journal of Scientific Research ISSN 1450-216X / 1450-202X Vol. 148 No 2 January, 2018, pp. 201-233 http://www. europeanjournalofscientificresearch.com

Bahjat R. J. Muhyedeen College of Science, Baghdad University, Iraq E-mail: [email protected]

Abstract

This paper is the sixthpart of a series of nine of QAMUQAMNMT2015Ver3. An innovative semi-empirical atomic mass formula has been derived to calculate quantized atomic masses more precisely than macro-micro formula and purely microscopic HF-self- consistent methods. It is based on the novel mass quantization and the variable neutron mass concepts of new nuclear theory NMT. It can calculate the atomic masses of non- existent isotopes based on the existing experimentally measured nuclides.The discrepancy(RMS) of the mass model is less than 335 keV for UQAM and 884 keV for QAM for the entire region of ground-state masses of 3160 nucleiranging from 1H to 118 Og.The quantized atomic masses of 15000 nuclei ranging from Z=1 to Z=200 have been calculated, 1230 nuclides of them belong to Z=81-99 (Tl-Es).The results are compared with - + those of other recent macroscopic–microscopic. S n, S p, β , β and α decay energies are also given.

Keyword: nuclear mass formula, neutron mass, atomic masses, new isotopes, superheavy nuclei, alpha decay

1. Introduction A. Background The explanation of the methods of the evaluation of the atomic masses has been discussed in details infour parts [1-4]of this series of 9 papers. In brief, the methods of theoretical calculations are of two types; hybrid of macroscopic and microscopic and pure HF-SCF models [ 5-51 ].All these theoretical methods calculate the binding energy first and then evaluate the neutral atomic mass. The binding energy are calculated from two parts which may be written as: B.E. = Emac (refined version of liquid drop) + Emic (shell+paring+Wigner terms) (1) And thetheoretical neutral atomic masses are evaluated from the following formula: MA = ZM H+NM N-B.E. (2) But none of these models can be usedwith total confidence due several deficiencies. Consequently, the accurate estimation of the atomic masses of the existent and non-existent isotopes in astrophysics is considered as unsolved problem . The output of most theoretical calculations cannot predict the atomic masses precisely which lead to improper alpha energies and half-lives. The atomic masses calculated by Wang-Audi-Wapstra,WAW et al. [25 ], Moller et al .[ 31 ] and Duflo-Zucker[ 39 ] failed to give the positive incremental difference in alpha energies between two sequential isotopes as we will see later.The mass evaluations usually use short-range connection between close lying neighbors isotopes. The researchers are looking for an extended complicate connectivity between multiple isotopes. The Quantized Atomic Masses of the Elements: Part-5; Z=81-99 (Tl-Es) 202

An immense project was setup in 2010 to solve this problem. In present project a newsemi- empirical polynomial 2 nd strategy is setup to adopt the measured atomic masses, inserting them into special quadratic equations and then extrapolate them to predict the accurate atomic masses for the non-existent element’ isotopes. In this manner, NMT is avoiding any theoretical treatment which lead to inaccuracy in the prediction processes and also use simple long-range relations amongthe element’s multiple isotopes. The new ansatz depends on the pure nuclear property i.e. atomic masses of the nuclei and avoids the external corrections used in the two main approaches in the theoretical description of nuclei. This article is part5 of the immense project. The aim of the project is to find out 1- a quantized mass formula QMF to the elements that have enough isotopes to setup a polynomial equation 2nd based on the available isotope masses (i.e. Z=1-107), it will be called isotopic quantized mass formula IQMF, 2- two quantized mass formula QMF to the elements that do not have enough isotopes (i.e. Z=108-118) to setup a polynomial equation that will create atomic masses for non-existent isotopes, they will be called analyticalAQMF, numerical quantized mass formula NQMF and total variable neutron mass TVNM, to generate a database for alpha energies for more than 1140 isotopes for Z=100-118, and 3- a quantized mass formula QMF to the non-existent elements that will create atomic masses for more than 4000 new non-existent isotopes, from the alpha energies database, it will be called energetic quantized mass formula EQMF (i.e. Period-8, Z=119-172 and period9, Z=173200 ). In present year 2017, the whole project is accomplished successfully. The polynomial equation of the 2 nd power generates the quantized atomic masses QAM while thepolynomial equation of 3rd up to 6 th power generates the unquantized atomic masses UQAM with RMS=335 keV. A novel Total Variable Neutron Mass TVNM method also used for calculation of QAM and UQAM. Both QAM and UQAM of the elements Z=1- 118 have been calculated. The QAM of the isotopes of the Period-8 Z=119-172 have been calculated in addition to QAM of the isotopes of 28 elements Z=173-200 of period-9.

B. Theory The standard model theory SMT essential concepts of the mass formula are based on the theory that both masses of protons and neutrons are invariant inside and outside of the nucleiand the energy has an equivalent mass based on mass-energy equivalence E=mc 2.Therefore, the binding energy of the nucleus is given by; B.E. = ZM H+NM N-MA. Where NMT supposes during the nucleosynthesis in the stars that the mass of the proton is invariant inside and outside of the nuclei while the mass of the neutron is variable inside the nuclei. NMT believes that no tiny mass fromany nucleon could be converted to any energy or to create the binding energyor vice versa.In this article, the mass quantization principle, MQP concept of the new theory is applied on the measured atomic masses M A (from IAEA ) to amend them and to extrapolate them.NMTalso uses its novel concept of mass-energy conformity MEC rather than mass-energy equivalence in explaining the B.E. NMT considers the B.E. and shell model as a confusion concepts (see next item-2.1). The application of MQP concept on the ∗ ∗ single / total variable neutron mass M/ N Minside the nuclei and theMEC on the binding energy B.E. help in calculating the quantized atomic masses M A of existent and non-existent isotopes which gives ∗ excellent results far from using B.E. terms.The single variable neutron mass is denoted by M to differentiate it from the mass of the free neutron M N.NMT shows that the atomic masses M A of the neutral nuclei can be calculated from summation of the total mass of proton and electrons (M H) and ∗ ∗ total mass of the corrected variable neutron masses M (i.e. M A=ZM H+N M) after manipulation far ∗ from B.E formula. In this manner, the corrected single variable neutron mass Mwill include the so- called B.E and Be(Z) term in form of mass rather than in form of energy and the atomic mass of the hydrogen M H will include the ZM e and ZM P. In 2008, Nuclear Magneton Theory of Mass Quantization-Unified Field , NMT concepts[ 52-54 ] considers all other heavier neutrinos as a multiple package of electron neutrino (i.e. magnetons). The reasons that NMT changed the “electron-neutrinos” name to “magnetons” name is that the magnetons are building blocks that form all the particles i.e.

203 Bahjat R. J. Muhyedeen electrons, muons, tauons etc. NMT believes that they have a magnetic dipole thus they called magnetons.

2. Method The general procedures and policies of calculation of the quantized atomic masses QAM are fully explicated here below:

2.1 Application of Mass Quantization Principle MQP on the Neutron NMT believes that; in severe circumstances such as in the stars, the bound neutrons are usually generated from fusion of protons (actually is due to disintegration of its nmtionic shells [ 54]) during the creation of nuclei releasing two positrons and neutrinos. NMT called the mass of the bound neutron ∗ as variable neutron mass M. NMT believes that there are no absolute stable nuclides at all and they 20 40 possibly live with t 1/2 ca 10 -10 y due to the unstable structure of the bound neutron, with unstable charge over mass[1-4,54]. NMT thinks that; contrary to the mass of the electron QM e and the proton QM p which they have a fixed quantized mass inside and outside the atom, the neutron has several stable ∗ variable masses M in the stable nuclei, which are called quantized QNM andunstablevariable masses ∗ Min the unstable poor and rich nuclei, which are called unquantized UQNM /UQNM respectively. In previous articles [ 1-4] many concepts and definitions explained such as VariableNeutron Masses(see Eq. (3)) , Neutron Mass Plateau(see Fig. 1&2), Neutron Mass Quadratic Equation, NMQE(see Eq. (4)) , the consonant and dissonant neutron masses CNM, DNM andIsotopic Quantized Mass Formula ∗ ∗ 2 IQMF(see Eq. (5)) . NMT sorts out the M values and nominates the M values based on their R values formed by theNMQE as dissonant neutron mass DNM (i.e. DNM ,DNM and DNM ) if they give ∗ 2 2 M-ln( A) graph with poor R values ((R <0.9999) and consonant neutron mass CNM (i.e. CNM ,CNM ∗ 2 2 and CNM ) if they give M-ln( A) graph with high R values (R ≥0.9999) ∗ M = (M A-ZM H)/N, N=number of neutrons (3) ∗ NMT usually correlates the single variable neutron masses, SVNM M, of the element’ isotopes versus their natural logarithm of mass number ln( A) for light and heavy elements to generate the Neutron Mass Quadratic Equation, NMQE (which gives a parabolic graph) with correlation coefficient R-squared, R 2. The values of R2 increase with increasing Z(see in Fig. 4-7). ∗ 2 2 M = α*ln (A ) - β*ln( A)+ γ R ≥0.9999 (4A) ∗ While it correlates the total variable neutron masses, TVNM NM , of the element’ isotopes versus their mass number (A) for Superheavy elements to generate Neutron Mass Quadratic Equation, NMQE (which gives a semi-linear graph, see Fig. 9B) with correlation coefficient R-squared, R 2. ∗ 2 2 NM = α*(A ) - β*(A)+ γ R ≥0.9999 (4B) Each element has its two equations of neutron mass quadratic equations NMQE, one for even nd ∗ and the other for odd isotopes. The polynomial equation of the 2 power of SVNM with ln( A);M- ∗ ln( A) graph; generates M which lead to the prediction of the quantized atomic masses QAM of light nd ∗ and heavy elements and polynomial equation of the 2 power of TVNM with ( A);NM -(A) graph; ∗ generates NM which lead to the prediction of the quantized atomic masses QAM of Superheavy elements. Two methods were used to calculate the unquantized atomic masses UQAM. First method rd th ∗ for Z=1-107; uses the polynomial equation 3 up to 6 power of SVNM with ln( A);M vs ln( A) to ∗ generate M which lead to the prediction of the UQAM. In case of UQAM, the acronym NMQE (Neutron Mass Quadratic Equation) is changed to NMPE (Neutron Mass Polynomial Equation), nd ∗ because it is non-quadratic. Second method for Z ≥93, uses the 2 power of TVNM with ( A);NM -A ∗ graph; to generate NM which lead to the prediction of the UQAM for Z=94-107.The first method has short range limit or extension in estimation of UQAM with a little bit lower RMS. The second method has long range limit or extension in estimation of UQAM a little bit higher RMS. TheUQAM of the elements Z=1-107 have been calculated The Quantized Atomic Masses of the Elements: Part-5; Z=81-99 (Tl-Es) 204

The QAM of the elements Z=1-118 have been calculated. Other various equations also tested to all isotopes of the elements Z=1-118, but showed low R 2. While Pearson correlation coefficient R ∗ 2 reflects the extent of a linear relationship between M and ln( A), R value can be interpreted as the ∗ proportion of the variance in M attributable to the variance in ln( A) in the NMQE. NMT inserts thedissonant orconsonant SVNM values into the isotopic quantized mass formula IQMF to get the initial atomic masses as follow: 2 QAM=ZM H + N( α*ln (A ) - β*ln( A)+ γ) (5) Where; α, β and γ are parameters depending on the neutron masses of the references point of the element. After substitution of the mass number of the isotopes into Eq. (5), the initial atomic masses will be calculated. The calculated atomic masses will be used to calculate the β-, β+, α-decay energies and which haveto give the positive difference in alpha energies between two sequential even-even and odd-odd mass number A; which denoted by the term ∆α (ee ,oo) as we will explain in the next paragraph. The UQAM are calculated from: UQAM=ZM H + N(NMPE), where the Neutron Mass rd th ∗ Polynomial EquationNMPE is polynomial of 3 up to 6 power for M-ln( A). In the second method, the UQAM are calculated from: UQAM=ZM H + (NME), where the neutron mass equation NME is nd ∗ polynomial of 2 power of TVNM for NM -A graph. The UQAM are very close to the IAEA and the RMS values become 9.3 keV for Z=100-118. NMT called the consonant CNM non-hermetic values of the alpha-emitter nuclides as Un- Generalized Neutron Masses values and denoted by UGNM. While NMT called the consonant CNM hermetic values of the alpha-emitter nuclides as Generalized Neutron Masses values and denoted by GNM (see Fig. 3). The GNM of known heavy isotopes will be used later for estimation of the GNM of non-existent elements’ isotopes. The GNM will generate QAM.NMT usually corrects the dissonant and consonant neutron masses; DNM and CNM values of the IAEA’ isotopes to achieve the harmonized graph with high R 2values (R 2>0.9999) to give NMQE that lead to provision of GNM. The correction of DNM and CNM values to GNM values is achieved through modifying them to give the neutron mass quadratic equation NMQE with higher R 2 exceed 0.9999 that achieve the following criteriaas shown in Scheme -1.The values of UQNM ,QNM and UQNM of the available isotopes from IAEA website (more than 3300 nuclides) of the elements Z=1-118 have been studied carefully.

Figure 1: The MQP and the relation between the UQNM , QNM , and UQNM and the decay mode

205 Bahjat R. J. Muhyedeen

Figure 2: The relation between the UQNM , QNM , and UQNM and the decay mode of oxygen isotopes which has 3 stable isotopes

Figure 3: NMT ’ neutron mass classification

Scheme 1: Flowchart shows the conversion of DNM or CNM to GNM

The Quantized Atomic Masses of the Elements: Part-5; Z=81-99 (Tl-Es) 206

The main criteria that bound the calculated GNM are; i. the even and odd curves of each element inside the graph have to show the parallelism with gap. Usually, inside the graph, the gap between isotopes of small A is larger than that in large A. The gap increase with increasing Z. This gap deforms the parallelism in the element of Z>130 and convert it to twisting in higher Z. Therefore, NMT replaces the treatment of SVNM by TVNM to avoid the deformation of the graphs. ii. the even curve should be lower than odd curve in even Z but vice versa for odd Z (see Fig. 4), iii. the calculated GNM should give harmonization curves of the sequential elements (see Fig. 8A & B), iv. theGNM valueshave to generate quantized atomic masses QAM that give the proper sequential values for β-, β+, α-decay energies without deviation and discontinuities, v. the calculated QAM should lead to the positive incremental difference in alpha energies between two sequential even-even and odd-odd mass number A; which denoted by the term ∆α (ee ,oo) . The ∆α (ee ,oo) values (i.e. violetvalues in the Tables 1-20 in the appendix-1)should be positive if the atomic masses are quantized. Otherwise, the atomic masses are not quantized. The second term is also considered during conversion CNMto GNM that the differences between each two sequential α-energy values of even-A and odd-A or vice versa ∆α (eo ,oe) has to be positive incremental values(i.e. blue values in the Tables 1-20in the appendix-1). All IAEA and the theoretical atomic masses, such as Moller and Duflo-Zucker etc., in the literature failed to give positive ∆α (ee ,oo) and ∆α (eo ,oe) . vi. the calculated QAM values have to be very close to the existing of IAEA, vii. the calculated QAM values should give the proper β- and β+ values in the element Z+1 and Z-1 respectively and proper α-energies values in Z and be suitable for α-decay energies in the next element Z+2. Normally, NMT avoids the modification of the QNM of the stable and relatively stable nuclides of Z=1-82.Achieving theseven criteria is a very challenging job because they conflict each other, consequently, this work requires 6 years of continuous work where more than 14000 isotopes are treated. The single variable neutron mass values are functions of Z, N,A,Eb/A,masses, half-lives, decay energies, magic numbers, deformations, shapes, sizes, shell structure and other properties of the nucleus. Therefore,NMT coins them as “ NucleusMaster Key ”. The Mass Quantization Principle MQP believes thatthe variable neutron masses inside the nucleus have to increase regularly with a fixed number of magneton packages in the nucleus with increasing the neutron number N. The regular increment in the neutron masses should create the DNM or CNM in different nuclides with increasing Z and N. That means there is a systemic increment in the neutron mass starting from neutron poor to neutron rich. NMT refers to the fixed increment in the neutron masses due to N increment as quantization process . The fixed increment in neutron masses in the isotopes of the element results in giving the positive incremental values in ∆α (ee ,oo) and ∆α (eo ,oe) . Furthermore, the NMT entitled theisotopic quadratic equations as Isotopic QuantizedMass Formula IQMF (Eq. 5) for the same reason and the atomic masses generated from GNM as quantized atomic masses QAM due to the quantization process. Fig. 8A shows how the IAEA values of DNM ofneutron poor have higher values than the DNM of the neutron rich which give arbitrary β-, β+, α decay energies for the element with Z=80-99.Fig. 8B shows the corresponding NMT treated consonant and hermetic GNM variable neutron masses values. NMT checked the neutron masses of more than 3430 isotopes of the elements Z=1-118 of IAEA {and also JAEA (Audi et al ., Private Communication (April 2011))} and found out that all of them are dissonant and non-hermitic neutron mass DNM (i.e. DNM,DNM and DNM)except seven elements; Z=92-99 (of 99 elements) show a consonant neutron masses CNM. They do not give sequential α energies.For example, the DNM, DNMand DNM of the isotopes of Z=33-72 and Z=79-92 displayed deviation in the parabolic curves that result in discontinuities in α energies.

207 Bahjat R. J. Muhyedeen

Fig. 9A shows the deviation (curvature, marked bya circle) of the IAEA neutron mass values which give discontinuities in α-decay energies for their isotopes.Fig. 9Bshows the generalized neutron masses of isotopes of the elements Z=81-99. The incorrectvalues of α-decay energies due to thedissonant and non-hermetic neutron massesspan from neutron poor to neutron rich passing the plateau of the stableisotopes.The discontinuities in α-decay energies of IAEA lead to curling curves of Qα vs N as seen in Fig. 26 in Appendix-1.The correction process for these neutron masses values will affect the values of the atomic masses of these isotopes of IAEA, therefore, NMT avoids a complete correction for Z=81-83 only to keep the difference between IAEA atomic masses of stable nuclides and NMT atomic masses as minimum as possible. The curvature in Fig.8A and in Fig.9A are due to underestimation of the IAEA atomic masses at the magic numbers 82 and 126 respectively.

Figure 4: The dissonant neutron mass DNM of even-odd nuclides of Aluminumfrom IAEA

Figure 5: The dissonant neutron mass DNM of even-odd nuclides of Cadmium from IAEA

Figure 6: The dissonant neutron mass CNM of even-odd nuclides of Rhenium from IAEA

The Quantized Atomic Masses of the Elements: Part-5; Z=81-99 (Tl-Es) 208

Figure 7: The consonant neutron mass CNM of even-odd nuclides of Einsteinium from IAEA

Figure 8: A-The dissonant neutron masses from IAEAand B- The generalized neutron masses of light elements’ isotopes after correction; Z= 80 -99 .

A. The IAEA dissonant neutron masses DNM of the elements; Z= 80 -99 isotopes

B. The corresponding NMT generalized neutron masses GNM of the elements; Z=80 -99 isotopes

209 Bahjat R. J. Muhyedeen

∗ ∗ The M-ln( A) graph (Fig.9A) is sensitive to the magic number while NM -Agraph (Fig.9B) ∗ isinsensitive. The NM -Agraph will generate the variable neutron mass matrix that can evaluate the atomic masses of non-existent isotopes as we will see in the forthcoming articles. The NMT called the calculated atomic which are very close to the IAEA as UQAM because they fail to give the positive incremental values in ∆α (ee ,oo) and ∆α (eo ,oe) . While NMT called the calculated atomic which are a littlebit far of the IAEA as QAM becausethey succeeded to give the positive incremental values in ∆α (ee ,oo) and ∆α (eo ,oe) . In item 2.7 we will see how the predicted atomic masses of the theoretical models fail to give the positive incremental values due to their reliance on IAEA or WAW database.

∗ Figure 9: The singlevariable neutron masses -ln( A)graph of isotopes of the elements Z=81-99 of IAEA is sensitive to the magic number 126. The circle in Figure-9A shows the curvature of the IAEA ∗ neutron mass values.Figure-9B shows the corresponding totalvariable neutron masses -Agraph which is insensitive.

A- The single neutron masses of the isotopes of the B- The totalneutron masses values of the isotopes of elements; Z=81-99 of IAEA . the elements; Z=81-99 of IAEA .

Magic Numbers NMT scrutinized the neutron magic numbers NMN of the neutrons in details from Z=2 up to 118, and found out they are active only in few nuclei (of small Z) but they are mostly inactive in the other nuclei. They seem as if they are stochastic complementary number with some selective proton numbers in some nuclei to give stable variable neutron masses more than phenomenological numbers. They do not have any influence at nuclei with Z greater than 90. For NMN; N=8, which is available in 13 elements, Z=2-14, has two stable nuclides only N, O. For NMN; N=20, which is available in 19 elements, Z=9-28, has five stable nuclidesonly S, Cl , Ar , K, Ca .For NMN; N=28, which is available in 21 elements, Z=12-32, has four stable nuclides Ti , V, Cr , Fe . For NMN; N=50, which is available in 24 elements, Z=27-50, has five stable nuclides Kr , Sr , Y, Zr , Mo . For NMN; N=82, which is available in 29 elements, Z=45-73, has six stable nuclides i.e. Ba , La , Ce , Pr , Nd , and Sm . For NMN; N=126, which is available in 18 elements, Z=76-93, has one stable nuclide Pb . For higher NMN; neither Z=114 nor N=184 shows stability effect in the superheavy isotopes of Z=100-200. NMT found similar results forthe known and the expected proton magic numbers PMN; Z=2, 8, 20, 28, 50, 82, 108, 114, 124, 126 and 164. The Quantized Atomic Masses of the Elements: Part-5; Z=81-99 (Tl-Es) 210

Only few nuclei with doubly MN are stable such 4He, 16 O, 40 Ca and 208 Pb while other nuclei with are unstable such Ni (2.1ms), Ni (6.07d), Ni (0.11s), Sn (1.16s), Sn (39.7s). The most important question is that why the graphs of E α vs N (neutron numbers) do not show a sharp peak after the NMN; 28, 50, 82, and 126 but they show a gradual peaks that the graph raise with 4-6 points (i.e. NMN+4-6) then comes down. This gradual peak clearly comes from the overestimation of the atomic masses rather than a magic number phenomena. If the magic numbers are really come out of the shell phenomenon then they have to be effective in that nuclei. When NMT treated the atomic masses to give the positive incremental values in ∆α (ee ,oo) and ∆α (eo ,oe) , these gradual peaks disappeared and the graphs became a smooth.Although the results of nuclear shell model of spherical nucleihas been proved by manyexperimental facts such as quadrupole moments, isotope abundances,binding energies, separation, pairing energies, nuclear radii and β,α-decay energies, but it does not mean these magic numbers grant the nuclei the stability. NMTconsiders the magic P and N as acomplementary numbers to achieve the stable variable neutron masses. Table-1 shows the doubly magic nuclei which is generated from combinations of the Z and N magic numbers. Only five stable isotopes are stable which explain the suspicion of their concepts. The microscopic-macroscopic models expected Z=114 and N=184 for the next doubly magic nucleus. NMT calculated the T 1/2 of this isotope -184 to be 3.01d, while next isotope -185 to be with T1/2 =102.1d. The non-relativistic mean-field models predict these numbers at Z=124 and 126 and N=184 are magic numbers. NMT calculated the T 1/2 of this isotope 124 -184 to be unstable and + decay with α=13144 MeV and β =4659 MeV, while the other isotope 126 -184 to be unstable and decay with α=14152 MeV and β+=6076 MeV. The relativistic mean-field models predict these numbers at Z=120 and N=172 are magic numbers. NMT calculated the T 1/2 of this isotope 120 -172 + to be unstable and decay with α=13602 MeV and β =6277 MeV, while the other isotope 120 -199 to be with T 1/2 =6158y. The theoretical studies predict the deformed nucleus at Z=108 and N=162 to be more stable. IAEA calculated the T 1/2 of this isotope -162 to be 3.1s, while NMT the isotope -174 to be 13.37d.

Table 1: The experimental doubly magic nuclei and the expected from theoretical studies

Z,N Z=2 Z=8 Z=20 Z=28 Z=50 Z=82 Z=108 Z=114 Z=120 Z=124 Z=126 Z=164 He-4 N=2 Stable He-8 O-16 Ca-28 N=8 119ms Stable NE O-28 Ca-40 Ni-48, N=20 NE Stable 2.1 ms Ca-48 Ni-56 Sn-78 N=28 1.9x10 19 y 6.08 d NE Ca-70 Ni-78 Sn-100 Pb-132 N=50 NE 0.11 s 1.16 s NE Sn-132 Pb-164 N=82 39.7 s NE Sn-164 Pb-196 Fl-228 N=114 160 ns 37 m NE Pb-208 Fl-240 N=126 Stable NE Hs-270 Fl-276 N=162 3.6 s 1.97 us

Hs-280 Fl-286 120 X-292 124 X-296 N=172 11.04h 0.16 s α=13602 α=15588 + + β =6277 β =9221 Fl-298 120 X-304 124 X-308 126 X-310 N=184 3.01 d α=11166 α=13144 α=14152 + + + β =1894 β =4659 β =6076

211 Bahjat R. J. Muhyedeen

Z,N Z=2 Z=8 Z=20 Z=28 Z=50 Z=82 Z=108 Z=114 Z=120 Z=124 Z=126 Z=164

Fl-310 120 X-316 124 X-320 126 X-322 N=196 α=5481 α=8348 α=10316 α=11318 + β=4765 247.89 d 2 m β =1652 124 X-360 126 X-322 164 X-400 β=18492 β=16614 α=20190 N=236 β+=1349 4 164 X-482 N=318 β,β+ emitter

2.2 The General Procedure for the Calculation of the Quantized Atomic Masses 1. Collecting the atomic masses and other properties values of the isotopes from IAEA for element Z=1-118 and from others such as JAEA, Wang-Audi-Wapstra (WAW) [ 25], and from Moller et al [31] for comparison. ∗ 2. Deriving the single variable neutron mass SVNM M from IAEA atomic masses. (see Eq. 3) ∗ 3. Using the polynomial functions to link M with ln( A) to setup the NMQE(see Eq. 4A)and the isotopic quantized mass formula IQMF (see Eq. 5) for the element Z=1-107 to calculate the QAM. The elements from Z=108-118 require different methods. NMT uses AQMF and NQMF as explained below. 4. Calculating the alpha energies of the isotopes for the element Z= 1 toZ= 99 consecutively. 5. Moving back from Z= 99 toZ= 1sequentially to calculate the positive ∆α (ee ,oo) values. The aim of this step is to depend on alpha energies of the appropriate alpha emitter element Z= 84 -99 6. Moving again from Z= 1 to Z= 99 to calculate the positive ∆α (eo ,oe) values. 7. Deriving and using the analytical mass formula AQMF and the numerical quantized mass NQMF formula to create the atomic masses for more than 700 isotopes belong to the element Z=108-118 as these elements don’t have enough isotopes (4 RP for even and/or 4RP for odd) to setup NMQE and IQMF. Each isotope can be created from its four ancestors. The alpha energies of the 700 isotopes have been calculated. The details of these procedures will be published soon. 8. The alpha energies of more than 1250 isotopes of the elements Z=100-118 with positive values for ∆α (ee ,oo) and ∆α (eo ,oe) used to setup the database for the element Z=119-200 of Periods-8 & 9. 9. Deriving and using the energetic quantized mass formula EQMF, which derive the SVNM &TVNM from the daughter to the mother keeping the positive values of ∆α (ee ,oo) and ∆α (eo ,oe) to secure the quantization of the atomic masses. EQMF succeeded in calculation of the quantized atomic masses QAM for Z=119-200. The results of items 7, 8 and 9 will be published in the next articles. The results were compared with Moller and DZ calculations.

2.3 The Special Isotopic Quantized Mass Formulafor the Elements Z=1-107 As we stated above that NMT’s procedure of calculation of the atomic masses is completely different from the SMT methods of determination or prediction of the atomic masses. NMT apply the Mass Quantization Principle MQP to the neutron mass which lead to generation of the DNM and CNM which they have to be converted to the generalized ( consonant hermetic) neutron masses GNM.The generated neutron masses GNMwill be substituted into the isotopic quantized mass formula IQMF (Eq. 5) to calculate the quantized atomic masses QAM. The quantized atomic masses of EinsteiniumEs are calculated below as an example below.

The Quantized Atomic Masses of the Elements: Part-5; Z=81-99 (Tl-Es) 212

I. Calculation of the Quantized Atomic Masses from IQMF NMT converts the CNM of 99 Es isotopes to GNM to calculate the quantized atomic masses. The precise quantized atomic masses QAM of the radioisotopes of 99 Es element is calculated in two steps. First , we have to calculate the generalized neutron masses GNM /GNM /GNM values as explained in the previous paragraph (see Scheme -1) to get two neutron mass quadratic equations NMQE; Odd-Even (Eq. 6) and Odd-Odd (Eq. 7) which are generated from Fig. 10 A&B, as follow: GNM = 0.022143171685457Ln( A)2 - 0.233762722898703 Ln( A) + 1.61103647390349, R² = 1.000 (6) GNM = 0.022560872766917Ln( A)2 - 0.238336286156576 Ln( A) + 1.62354800693296, R²=1.000 (7) The calculated values GNM /GNM /GNM of 50 isotopes are listed in Table-2. Column 4, shows the difference between the values of the dissonant neutron masses DNM of IAEA and the generalized neutron masses GNM of NMT. The red valuesGNM refer to neutron-rich equation, the green valuesGNM refer to neutron-poor while the blue values refer to stable nuclides. Second , we insert the GNM /GNM /GNM values into the isotopic quantized mass formula 2 IQMF Eq. 5, QAM=ZMH + N(α*ln (A ) - β*ln( A)+ γ) as follow: For example, the quantized atomic masses QAM of the NR 99 Es-272 and NP 99 Es-225and are calculated as follow: QAM =99 MH + 173 (0.996458461219408 , from Table-2) (8) = 272.16199198173 u QAM =99 MH + 125 (0.994498632356545 , from Table-2) (9) = 225.08150586770 u The calculated quantized atomic masses QAM values of 50 isotopes are listed in Column 4 in Table-4. The quantized atomic masses QAM for new non-existent such as 224 Es -240 Es and 258 Es -273 Es etc. have been calculated using equations 6-9 as seen in the Table-4. Column 2, MIAEAQAM , shows the difference between the unquantized masses of the IAEA and the quantized masses of NMT. Generally, the differences become larger when we go up or down far from the quantized masses of stable isotopes. NMT discovered that most of IAEA atomic masses of far neutron-poor and far neutron-rich isotopes are overestimated by nuclear workers which are listed by the tables of IAEA website and also in JAEA and NNDC websites.

Table 2: The CNM (from IAEA ) and GNM (from NMT ) of Einsteinium’ isotopes

The differences CNM /CNM GNM /GNM variable ∗ ∗ between M and No Nuclide variable neutron neutron mass, GM ∗ Half-lives A N ∗ GM mass, CM (u) (u)* ∗ ∗ ∆Mn=CM - GM 1 99Es-224 0.994478356773127 224 125 2 99Es-225 0.994498632356545 225 126 3 99Es-226 0.994532544879650 226 127 4 99Es-227 0.994553918319317 227 128 5 99Es-228 0.994589708655769 228 129 6 99Es-229 0.994612206690689 229 130 7 99Es-230 0.994649766096728 230 131 8 99Es-231 0.994673415060098 231 132 9 99Es-232 0.994712637845529 232 133 10 99Es-233 0.994737463666697 233 134 11 99Es-234 0.994778247088751 234 135 12 99Es-235 0.994804275295530 235 136 13 99Es-236 0.994846519457240 236 137 14 99Es-237 0.994873775178549 237 138 15 99Es-238 0.994917382931423 238 139 16 99Es-239 0.994945890900218 239 140 17 99Es-240 0.994990767750991 240 141 18 99Es-241 0.995027336684718 0.995020552307456 0.000006784377 8s 241 142

213 Bahjat R. J. Muhyedeen

The differences CNM /CNM GNM /GNM variable ∗ ∗ between M and No Nuclide variable neutron neutron mass, GM ∗ Half-lives A N ∗ GM mass, CM (u) (u)* ∗ ∗ ∆Mn=CM - GM 19 99Es-242 0.995069152512098 0.995066606328712 0.000002546183 13.5s 242 143 20 99Es-243 0.995102998675208 0.995097691423677 0.000005307252 21s 243 144 21 99Es-244 0.995146240063655 0.995144833168158 0.000001406895 37s 244 145 22 99Es-245 0.995181991844041 0.995177242366725 0.000004749477 1.1min 245 146 23 99Es-246 0.995225971491360 0.995225384785142 0.000000586706 7.5min 246 147 24 99Es-247 0.995263133961013 0.995259141270489 0.000003992691 ND 247 148 25 99Es-248 0.995307334290134 0.995308199632667 -0.000000865343 24min 248 149 26 99Es-249 0.995344885394867 0.995343326210008 0.000001559185 102.2min 249 150 27 99Es-250 0.995390290127351 0.995393218029203 -0.000002927902 8.6h 250 151 28 99Es-251 0.995429706547566 0.995429737129887 -0.000000030582 33h 251 152 29 99Es-252 0.995479095910000 0.995480382090123 -0.000001286180 471.7d 252 153 30 99Es-253 0.995520438469026 0.995518315775853 0.000002122693 20.47d 253 154 31 99Es-254 0.995569961343419 0.995569635662140 0.000000325681 275.7d 254 155 32 99Es-255 0.995612799789936 0.995609005629292 0.000003794161 39.8d 255 156 33 99Es-256 0.995661915982357 0.995660924260580 0.000000991722 25.4min 256 157 34 99Es-257 0.995704435501456 0.995701751844611 0.000002683657 7.7d 257 158 35 99Es-258 0.995754195009367 258 159 36 99Es-259 0.995796501189294 259 160 37 99Es-260 0.995849396583567 260 161 38 99Es-261 0.995893201986506 261 162 39 99Es-262 0.995946479154370 262 163 40 99Es-263 0.995991804060123 263 164 41 99Es-264 0.996045394336395 264 165 42 99Es-265 0.996092258682073 265 166 43 99Es-266 0.996146095137197 266 167 44 99Es-267 0.996194518521873 267 168 45 99Es-268 0.996248535908868 268 169 46 99Es-269 0.996298537598248 269 170 47 99Es-270 0.996352672301645 270 171 48 99Es-271 0.996404271232746 271 172 49 99Es-272 0.996458461219408 272 173 50 99Es-273 0.996511676005240 273 174 In column 3, GNMred color values are neutron rich isotopes, GNMgreen color are neutronpoor isotopes

Figure 10A: The generalized neutron mass of Einsteinium (even)

The Quantized Atomic Masses of the Elements: Part-5; Z=81-99 (Tl-Es) 214

Figure 10B: The generalized neutron mass of Einsteinium (odd)

II. Calculation of the QAM from Isobaric Quantized Formula ISQMF NMT also able to calculate some QAM for neutron poor isotopes from the isobaric quantized mass formula ISQMF Eq. 10. TheBi-209 isobars series (from NMT values) and Bi-209 (from IAEAvalues) were selected as examples to evaluate the QAM of Th-209 and Pa-209 as seen in Figure-11A and UQAM of Th-209 and Pa-209 as seen in Figure-11B. The GMN and CNM values for Th-209 and Pa- 209 are calculated from Eq. 10A & B respectively to be 0.994235098507841,0.994228948409664, 0.994205087402065 and 0.994189022625863 respectively. The corresponding QAM and UQAM of Th-209are 209.01822962313 u and 209.01749776145 u.The corresponding QAM and UQAM of Pa- 209are 209.02827824637 u and 209.02638260278 u. NMT -GNM = 0.031461469621718Ln( Z)2 - 0.286204872016635 Ln( Z) + 1.6450616807845, R² = 0.9997 (10A) IAEA -CNM = 0.022522736573592Ln( Z)2 - 0.206558174891550 Ln( Z) + 1.46765458554642, R² = 0.9999 (10B)

Figure 11A: The generalized neutron mass of Bi-209 isobars

215 Bahjat R. J. Muhyedeen

Figure 11B: The consonant neutron mass of Bi-209 isobars

2.4. Calculation of the Theoretical β-, β-, EC Energies

The beta energies are calculated from SMT (based on mass defect MD ,∆MA), NMT (based on neutron mass defect NMD ,∆Mn) and standard energy of formation of nuclide E , SEFN (based on a specific perception that in severe circumstances such as in the stars, the bound neutrons are usually generated from fusion of protons during the creation of nuclei releasing two positrons and neutrinos).The three methods give the same results. The beta, EC-decay energy values are listed in the Tables 1-20 in the appendix-1. - - A SMT-MD; (based on mass defect MD,∆MA) The Q-value of β , β , EC-decay can be calculated from the mass defect. SMT-MD ; β-: Q - = M(A,Z)-M(A,Z+1); β+: Q + = M(A,Z)-M(A,Z-1) (11) B NMT-NMD ;(based on neutron mass defect NMD,∆Mn) - - 1. β -decay: The general formula of NMD (∆Mn) for β -decay is given by: ∆Mn =[(M A-ZM H)M – (M A-Z1MH)D] (12) The term (M A-ZM H)Mand(M A-Z1MH)D will give the total mass of neutrons in the mother M and the daughter D respectively [ 54 ]. + + 2. β -decay: The general formula of ∆Mn for β -decay is given by: ∆Mn =[(M A-Z1MH)M – (M A-ZM H)D] (13) 3. EC-decay: The general formula of ∆Mn for EC-decay is given by: ∆Mn =[(MA-Z1MH)M) - (M A-ZM H)D] (14) Thus, both positron and EC decay follow that same equation.Both SMT – MD and NMT – NMD could not set up a sharp criterion to differentiate between β+ and EC. In the following item, we will see how the new nuclear concept will sort out this issue. C NMT-SEFN : Standard Energy of Formation of Nuclide E NMT proposed a standard energy of formation of nuclide , SEFN , ∆E (nucleosynthesis) in the stars as a new concept which is based on neutron mass quantization [ 1-4,54 ]. As explained previously, the protons and the electrons are stable with fixed mass outside the nuclei and the atoms in the normal circumstances. In severe circumstances such as in the stars, the bound neutrons are usually generated from fusion of protons during the creation of nuclei releasing two positrons and neutrinos. ∗ NMT called the mass of the bound neutron as variable neutron mass M as explained in item 2.1. The energy released or consumed from nucleogenesis process of the nucleus is called the standard energy of formation of nuclide, SEFN ∆E (similar to standard enthalpy of formation ∆H in chemistry). The SEFN concept does not focus on the number of the protons and electrons of the created nuclide. It is different from binding energy concept B.E and it has lower values than B.E by 0.81- 0.89 approximately as seen in Figure-12. The Quantized Atomic Masses of the Elements: Part-5; Z=81-99 (Tl-Es) 216

It is supposed that the binding energy BE explain the easy of formation; nucleosynthesis or nucleogenesis, and the degree of the stability of the nuclide, but it seems not. The well-known statement “ the energy liberated in the formation of nucleus from its component nucleon is a measure of stability of that nucleus ” is incorrect. In other words, the higher the value of B.E, does not mean the higher the stable nuclide is. Both the B.E and SEFN give higher energies values to unstable nuclides (which form 50% of total nuclides) that belong to Z=1-99 rather than to stable nuclides. For example, both indicate that the 8Be and 218 U nuclides have the highest B.E and SEFN among Be and U isotopes respectively. SEFN has two advantage over B.E that it can calculate the Q-values for all nuclear processes and it can give a sharp criterion to EC-decay, while B.E failed. The comparison between binding energies B.E and SEFN energies for Ra and U isotopes are illustrated in Figures 13&14. The application of SEFNon all nuclear process calculation gives identical results to SMT calculations while the binding energies cannot give the correct Q-values for β-, β-, EC- decay processes.

Figure 12: Comparison of binding energy of IAEA with SEFN of NMT values of Z=1-100

Figure 13: Comparison of binding energy of IAEA with SEFN of NMT values of Ra isotopes

217 Bahjat R. J. Muhyedeen

Figure 14: Comparison of binding energy of IAEA with SEFN of IAEA and NMT values of U isotopes

The general formula for ∆E is; ∗ ∗ ∆E =N M - (N M+NM e) x 931.5 MeV (15) ∗ ∗ Equation No 15 can be written in another mode, where N M - (N M+NM e) is equal to N(M p- ∗ ∗ Me) = (M A-ZM H) + NM e and after few substitutions to replace M by M H and the Mby(M A-ZM H)the final form is given as follows: ∆E =AM H - (M A+2NMe) x 931.5 MeV (16) Where A= mass number, MH=1.0078250322323 u, For example, the standard energy of formation E of He can be calculated as follow; ∗ ∗ = [2 M-(2 M+2M e)] i.e. [2 x 1.007276466812 u - (2 x 0.993476593 u + 2 x 0.0005485799095 u)] 2 ∆E =24.6870 MeV/c ∗ The E can be calculated also from the variable neutron mass M only as follow: ∗ E =N(1.00672787241186-M) x 931.4940023 MeV (17) ∗ Therefore, any nuclide with variable neutron mass Mexceeds 1.00672787241186 will have a negative E value. The binding energy may be calculated also from E as follow: B.E.=(0.00193704343814N+SEFN (u)) x 931.4940023 MeV (18) For any nuclear process A+B →C+D , the energy change for the nuclear reaction can be calculated as follow: ∆E =∑ ∆E ( + ) -∑ ∆E ( + ) (19) The SEFN concept is completely different from SMT’s ∆MAand NMT’s ∆Mnin two points: first , it uses the standard energy of formation E of the nuclides in the calculation rather than the mass defect in SMT or the neutron mass defect in NMT; second , it deducts the reactants from the products unlike SMT and NMT which deducts the products from the reactants. - 1. In negatron decays, the Q-value of β -decay can be calculated from ∆E , where ∆E, < ∆E, . ∆E = ∆E (B)-∆E (A) -1.0219978922 (20) + 2. In positron decay, Q-value of β -decay can be calculated, where ∆E, < ∆E, . - + The ∆E of the mother in β and β decay should be smaller than the ∆E of the daughter. ∆E =∆E (B)-∆E (A)+ 1.0219978922 (21)

The Quantized Atomic Masses of the Elements: Part-5; Z=81-99 (Tl-Es) 218

2 Table 3: ∆ values (MeV/c ) for EC-decay of the neutron poor isotopes of the elements Z=81-99 * EC cannot happen because for mother is less than for daughter

Electron Capture Criteria Electron Capture Criteria No Nuclear Process: EC-decay IAEA SEFN ∆E No Nuclear Process: EC-decay IAEA SEFN ∆E * 1 Tl + e → Hg + υ Yes No 2 Tl + e → Hg + υ 100% Yes * 3 Tl + e → Hg + υ Yes No 4 Pb + e → Tl + υ 100% Yes 5 Pb + e → Tl + υ 100% Yes 6 Pb + e → Tl + υ 100% Yes 7 Pb + e → Tl + υ 100% Yes 8 At + e → Po + υ 58.2% Yes * * 9 Rn + e → At + υ 72.6% No 10 Ac + e → Ra + υ 90% No * 11 Th + e → Ac + υ 10% Yes 12 Pa + e → Th + υ 98% No 13 Pa + e → Th + υ 99% Yes 14 U + e → Pa + υ 5% Yes * 15 U + e → Pa + υ 80% No 16 U + e → Pa + υ 100% Yes * * 17 Np + e → U + υ 60% No 18 Np + e → U + υ 98% No * 19 Np + e → U + υ 100% No 20 Np + e → U + υ 100% Yes 21 Np + e → U + υ 86% Yes 22 Pu + e → Np + υ 90% Yes 23 Pu + e → Np + υ 94% Yes 24 Pu + e → Np + υ 100% Yes * * 25 Am + e → Pu + υ 100% No 26 Am + e → Pu + υ 97% No * * 27 Am + e → Pu + υ 100% No 28 Am + e → Pu + υ 99% No * 29 Am + e → Pu + υ 100% Yes 30 Am + e → Pu + υ 100% No * 31 Cm + e → Am + υ 96% Yes 32 Cm + e → Am + υ 100% No * 33 Cm + e → Am + υ 99% Yes 34 Bk + e → Cm + υ 99% No * 35 Bk + e → Cm + υ 100% No 36 Bk + e → Cm + υ 100% Yes * 37 Cf + e → Bk + υ 64% No 38 Cf + e → Bk + υ 100% Yes * * 39 Es + e → Cf + υ 96% No 40 Es + e → Cf + υ 60% No * * 41 Es + e → Cf + υ 100% No 42 Es + e → Cf + υ 97% No 43 Es + e → Cf + υ 99.5% Yes 44 Fm + e → Es + υ 88% Yes

3. In EC-decay, the ∆E of the mother should be larger than the daughter which is a sharp criterion for EC-decay, where ∆E, > ∆E, .In EC decay we add 2M e to the right side (products) to get Q EC value (same as in b). It is different procedure from SMT and NMT. SEFN add 1.0219978922 MeV to the daughter because the ∆E of the mother is larger than ∆E of the daughter . EC cannot happen because E for mother is less than for daughter. ∆E =∆E (B)-∆E (A) + 1.0219978922 (22) The Q EC energy values for isotopes of the elements Z=81-99 are listed in the Tables-3.

2.5 Proton and Neutron Separation Energies

The proton S p and neutron S n separation energies are calculated from SMT (based on mass defect MD ,∆MA), NMT (based on neutron mass defect NMD ,∆Mn) and standard energy of formation of nuclide E , SEFN [54]. The three methods give the same results: A SMT-MD ; the proton S p and neutron S n separation energies can be derived from the following combinations of atomic masses as follow: Sn= -M(A,Z)+M(A-1,Z)+N (23) Sp= -M(A,Z)+M(A-1,Z-1)+H (24) where H and N are the mass of the hydrogen atom and the neutron respectively. The proton separation energies (S p) generally increase with increasing neutron number (N) and neutron separation energies (S n) increase with increasing proton number (Z). For a given Z, S n is larger for even N compared to that for odd N. Similarly, for a given N, S p is larger for even Z compared to that for odd Z. This pairing of like nucleons causes e-e nuclei to be more stable than e-o or o-e nuclides which, in turn, are more stable than o-o nuclei. The pairing energies of P and N are usually calculated from proton S p and neutron S n separation energies. The values of the proton S p and neutron S n separation energies are

219 Bahjat R. J. Muhyedeen presented in the Figures 21-24 in Appendix-1, where they show that the more energy is required to remove neutron when N even than odd. B NMT -NMD : The general formula of ∆Mn for the neutron S n separation energies and proton S p (MeV) are given by: Sn=∆Mn =[-(M A-ZM H)(Z,A) + (M A-ZM H)Z,(A-1) +M N] (25) SP=∆Mn =[-(M A-ZM H)(Z,A) + (M A-ZM H)(Z-1),(A-1) ] (26) C NMT -SEFN : The general formula of ∆Mn for the neutron S n separation energies and proton S p (MeV) are given by: ∆E, =[( ∆E )M,(Z,A) - (∆E )D,(Z ,A-1) ]+1.80435] (27) ∆E, =[( ∆E )M,(Z,A) - (∆E )D,(Z-1,A-1) ] (28)

2.6 Calculation of Energies and ∆α (ee,oo) and ∆α (eo,oe) of Z=81-99 Isotopes The alpha energy are calculated from SMT (based on mass defect MD ,∆MA), NMT (based on neutron mass defect NMD ,∆Mn) and standard energy of formation of nuclide , E , SEFN . The three methods give the same results: SMT-MD;The Q-value of β-, β--decay (MeV) can be calculated from the mass defect SMT-MD ; α: = M(A,Z)-M(A,Z-2)-Mα (29) NMT-NMD ; = ∆Mn =[(M A-ZM H)M – {(M A-ZM H)D + (M A-ZM H)α}] (30) NMT-SEFN ; ∆E =∑ ∆E ( + ) -∑ ∆E ( + ) , =0 (31) Where M=mother, D=daughter, α=alpha Following the steps of the main criteria from i to vii the theoretical alpha energies of Eswere calculated with positive values of the two terms ∆α (ee,oo) and ∆α (eo,oe) . Thecalculated QAM from GNM valuesresult in the positive values in ∆α (ee,oo) and ∆α (eo,oe) as seenin the Table-4 (see 8th and 9th columns)if the atomic masses are quantized. Otherwise, the atomic masses are not quantized. The th th 7 and 10 columns show that there are few alpha energy in red color are unquantized in NMT - + and IAEA. The calculated QAM values finally give the proper sequential values for β , β , energies without deviation and discontinuities as seen in Table-4 and illustrated in Fig. 25-26 in comparison with WAW E α (see Fig. 27) in the appendix-1.

Table 4: The Quantized Atomic Masses QAM of Einsteinium Isotopes

NMT-MQ, QAM-Z-99 2 IAEA NMT QAM= ZMH + N(α*ln (A ) - β*ln( A)+ γ) ∆α ∆α ∆M= IAEA- Isotope IAEA NMT-QAM T β- β+ α (ee, β- β+ α (ee, QAM 1/2 oo) oo) 1 99Es-224 224.08447278741 11183 8393 13 2 99Es-225 225.08150586770 9535 8390 23 3 99Es-226 226.08031139049 10590 8380 29 4 99Es-227 227.07757973564 8867 8367 39 5 99Es-228 228.07675060736 9981 8351 45 6 99Es-229 229.07426506056 8194 8328 55 7 99Es-230 230.07379754944 9356 8306 62 8 99Es-231 231.07156897870 7517 8274 71 9 99Es-232 232.07145902423 8714 8244 79 10 99Es-233 233.06949832211 6836 8203 88 11 99Es-234 234.06974154775 -6231 8055 8165 96 12 99Es-235 235.06805963096 -7483 6152 8115 104 13 99Es-236 236.06865135641 -5549 7381 8069 113 14 99Es-237 237.06725916541 -6813 5465 8011 121 15 99Es-238 238.06819441824 -4861 6691 7956 131 16 99Es-239 239.06710291680 -6124 4776 7890 138 17 99Es-240 240.06837644366 -4167 5985 7825 148 18 99Es-241 241.068560000 241.06759661843 0.00096338 8s -5263 4536 8250 178 -5415 4084 7752 155 19 99Es-242 242.069567000 242.06920289578 0.00036410 13.5s -3598 5415 8160 223 -3466 5264 7676 166 20 99Es-243 243.069510000 243.06874575578 0.00076424 21s -4616 3757 8072 163 -4688 3390 7596 173 The Quantized Atomic Masses of the Elements: Part-5; Z=81-99 (Tl-Es) 220

NMT-MQ, QAM-Z-99 2 IAEA NMT QAM= ZMH + N(α*ln (A ) - β*ln( A)+ γ) ∆α ∆α ∆M= IAEA- Isotope IAEA NMT-QAM T β- β+ α (ee, β- β+ α (ee, QAM 1/2 oo) oo) 21 99Es-244 244.070883000 244.07067900015 0.00020400 37s -2939 4548 7937 196 -2760 4527 7510 184 22 99Es-245 245.071249000 245.07055557631 0.00069342 1.1min -3819 2981 7909 447 -3941 2695 7424 190 23 99Es-246 246.072896000 246.07280975419 0.00008625 7.5min -2286 3810 7741 581 -2049 3775 7326 202 24 99Es-247 247.073622017 247.07303109880 0.00059092 ND -3095 2475 7462 526 -3175 1998 7234 208 25 99Es-248 248.075471000 248.07559993604 -0.00012894 24min -1598 3061 7160 327 -1333 3008 7124 220 26 99Es-249 249.076411000 249.07617712227 0.00023388 102.2min -2344 1450 6936 338 -2390 1301 7026 225 27 99Es-250 250.078612000 250.07905411318 -0.00044211 8.6h -847 2055 6833 44 -612 2225 6904 238 28 99Es-251 251.079993586 251.07999823451 -0.00000465 33h -1440 377 6598 -141 -1587 603 6801 243 29 99Es-252 252.082979865 252.08317665056 -0.00019679 471.7d 478 1260 6789 174 113 1428 6666 257 30 99Es-253 253.084825715 253.08449882025 0.00032689 20.47d -334 -288 6739 303 -765 -95 6558 261 31 99Es-254 254.088022199 254.08797171840 0.00005048 275.7d 1088 650 6616 389 843 616 6409 275 32 99Es-255 255.090274958 255.08968306894 0.00059189 39.8d 290 -720 6436 386 76 -793 6297 279 33 99Es-256 256.093599000 256.09344329968 0.00015570 25.4min 1700 146 6227 1577 -211 6134 294 34 99Es-257 257.095979000 257.09555498222 0.00042402 7.7d 813 6051 936 -1491 6018 297 35 99Es-258 258.09959519726 2314 -1052 5841 312 36 99Es-259 259.10211838106 1814 -2188 5721 315 37 99Es-260 260.10643104072 3055 -1908 5528 331 38 99Es-261 261.10937691258 2710 -2884 5406 333 39 99Es-262 262.11395429293 3800 -2778 5198 350 40 99Es-263 263.11733405663 3625 -3580 5073 351 41 99Es-264 264.12216825628 4547 -3662 4848 368 42 99Es-265 265.12599313199 4558 -4273 4722 369 43 99Es-266 266.13107607868 5297 -4560 4480 387 44 99Es-267 267.13535730245 5509 -4965 4353 388 45 99Es-268 268.14068075937 6050 -5472 4092 406 46 99Es-269 269.14542958247 6479 -5655 3965 406 47 99Es-270 270.15098515435 6806 -6398 3686 425 48 99Es-271 271.15621284280 7466 -6343 3559 424 49 99Es-272 272.16199198173 7563 3262 50 99Es-273 273.16770981568 8472 3134 In column 4, red color QAM values are neutron rich isotopes, green color QAM are neutron poor isotopes. All the atomic masses of einsteinium are QAM.

2.7 Comparison of Atomic Masses with Literature The atomic masses calculated by IAEA, JAEA, Wang-Audi-Wapstra et al ., WAW [ 25], and by Moller et al. [31] have been investigated and compared with present work NMT calculation. The WAW values are very close to IAEA values and both of them give limited isotopes to each element. WAW calculations are highly corrected based on experimental nuclear data such as atomic masses and nuclear reactions etc. Although Moller et al values are based on theoretical Macro-Micro MM equations but also, they did several corrections and amendment during three decades. The neutron masses values derived from IAEA, WAW and Moller are not able to give to the positive incremental difference in alpha energiesi.e. ∆α (ee,oo) and ∆α (eo,oe) as seen in 11 th and 12 th columns of Table-4 which are responsible for generating the proper data base Z=1-118 for atomic calculation of isotopes with Z=119-200. The neutron masses values of IAEA and Moller show high deviation from NMT values especially in the far neutron poor and neutron rich regions (see Fig. 15A&B). NMT attributed the deviation of Moller values to the improper parameters of macro-micro formula. Figures 16 and 17 shows the accuracy of the current calculations in comparison with the literature. The MM describes the nuclei as macro model (such as liquid drop etc.) from standpoint and the micro model (such as shell structure etc.) point of view and thus MM will give a confused model rather than hybrid model.Moller model gives overestimated atomic mass with increasing Z. For example, NMT calculated the quantized atomic mass QAM for ; M A= 297.24405819090 u, while Moller calculation gives 297.24797796322 with ∆M=0.00391977232 u and Duflo-Zucker, DZ [ 39 ] calculation gives 297.23962686328 with ∆M=0.00443132762 u. The maximum mass number A calculated by Moller was A=339 and A=297 by Duflo-Zucker while NMT can reach above 560 and no limit. Table-6 shows a

221 Bahjat R. J. Muhyedeen sample for NMT calculation for the accurate atomic masses, decay energies and their estimated α partial ℎ half-lives for few isotopes belong to Z=118-147. Koura-Tachibana et al. derived a nuclear mass formula and improved in 2005 and termed it as “KTUY” [ 41 ] and estimated the Q α for , , , 6.84, 8.12, 14.45, and 14.12 MeV respectively compared with present work calculation 6.429, 8.289, 14.152, and -11.845 MeV. DZ calculation gives 7.386 MeV for only and Moller calculation gives 6.915, 8.995 and 11.275 MeV for , , , only. KTUY is close to NMT only in the first three isotopes but there is a big difference in the fourth isotope. All theoretical calculations give inconsecutive alpha energies for Z>118.

Table 6: The NMT atomic masses, decay energies and their estimated α partial half-lives of few isotopes from Period-8

- + Isotope Atomic masses Z A N β β SP RF VSS 118-Og-310 310.25031533241 118 310 192 -487 -2327 8359 5.13E-01 1.20E-01 4.05E-01 120-VIII-12-315 315.26502139407 120 315 195 -1205 -2637 8603 1.50E+00 4.64E-01 7.45E-01 122-VIII-17-323 323.29077813275 122 323 201 -724 -3865 8054 1.34E+03 3.72E+02 6.66E+02 137-VIII-19-368 368.42552059672 137 368 231 -454 -3697 6514 1.46E+17 4.57E+16 1.24E+17 139-VIII-21-378 378.45346323132 139 378 239 -974 -7520 4587 4.18E+34 1.37E+34 4.98E+34 147-VIII-26-395 395.49123504109 147 395 248 -1079 -594 5463 4.13E+31 1.66E+33 1.69E+30 SP=Sobiczewski-Parkhomenko Formula [ 55], RF=Royer Formula [ 56 ], VSS=Viola-Seaborg-Sobiczewski Formula [ 57 ]

Another example, Muntian et al [42] calculated the alpha energies for 119 starting from A=291 up to 307, the values of Alpha for nuclides with A=291-297 are 12.89, 12.73, 12.62, 12.38, 12.55, 12.65, and 12.86 MeV respectively. It is very clear that they decreased to the minimum at 12.38 then increased up to 12.86 MeV. Always Moller atomic masses are higher than Muntian et al and both are higher than the QAM of NMT. For example, the atomic masses for 292 120 and 297 120 are calculated as 292.2286 5416852 ,292.2274 6253451 ,292.2257 6296088 and 297.231 50979596 ,297.230 71537329 ,297.22 834165491 by Moller, Muntian and NMT respectively.Table-7 lists alpha energies for Z=119 and Z=120 of the theoretical models of Duflo-Zucker,Muntian et al ,Moller et al , and Smolanczuk et al . It is supposed that the values of the alpha energies of the isotopes of the same element decrease with increasing mass number while the calculations of Duflo-Zucker,Muntian et al ,Moller et al , and Smolanczuk et al [58 ]showed an arbitrary alpha values as seen in Figures 19 and 20.

The Quantized Atomic Masses of the Elements: Part-5; Z=81-99 (Tl-Es) 222

Figure 15A: Comparison of the neutron masses among IAEA, Moller and present work NMT, Z=80-90

223 Bahjat R. J. Muhyedeen

Figure 15B: Comparison of the neutron masses among IAEA, Moller and present work NMT, Z=90-99

The Quantized Atomic Masses of the Elements: Part-5; Z=81-99 (Tl-Es) 224

Figure 16: Comparison of the NMT- UQAM and QAM with other models H. Geissel, Yu.A. Litvinov et al, Nucl. Phys. A746 (2004) 150c

Figure 17: Mass Difference among DZ, Moller and NMT in relation to WAW, Z=81-99

225 Bahjat R. J. Muhyedeen

Table 7: The theoretical alpha decay energies of few isotopes from Z=119 and 120

Smola Isotope A D-Z Muntian Moller NMT Isotope A D-Z Muntian Moller NMT nczuk 119X-291 291 13434 12890 13235 13102 120X-292 292 13787 13460 13775 13590 13602 119X-292 292 13188 12730 13075 12917 120X-293 293 13530 13340 13645 13432 119X-293 293 12943 12620 12915 12736 120X-294 294 13281 13240 13485 13420 13223 119X-294 294 12706 12380 12845 12549 120X-295 295 13033 13010 13455 13047 119X-295 295 12472 12550 12935 12358 120X-296 296 12794 13230 13585 13400 12833 119X-296 296 12245 12650 12975 12168 120X-297 297 12555 13490 13645 12651 119X-297 297 12020 12860 12895 11968 120X-298 298 13440 13235 13360 12429 119X-298 298 12590 13085 11773 120X-299 299 13230 13725 12241

119X-299 299 12630 13075 11564 120X-300 300 13110 13695 13090 12018

119X-300 300 12600 13025 11367 120X-301 301 13110 13615 11824

119X-301 301 12590 13075 11149 120X-302 302 13080 13545 13070 11596

119X-302 302 12560 13045 10948 120X-303 303 13050 13505 11396

119X-303 303 12560 13105 10722 120X-304 304 13070 13545 13120 11164

119X-304 304 13510 13855 10518 120X-305 305 13990 14255 10957

119X-305 305 13270 13855 10283 120X-306 306 13730 14275 13530 10721

119X-306 306 13160 13925 10074 120X-307 307 13650 13615 10508

119X-307 307 13090 13385 9832 120X-308 308 13560 12955 10268

Figure 18: Comparison of the NMTQAM’E α with other models, Z=119

The Quantized Atomic Masses of the Elements: Part-5; Z=81-99 (Tl-Es) 226

Figure 20: Comparison of the NMT QAM’E α with other models, Z=120

Summary Two methods were used to calculate the unquantized atomic masses UQAM. First method for Z=1- rd th ∗ ∗ 107; uses the polynomial equation 3 up to 6 power of SVNM with ln( A);M vs ln( A) to generate M which lead to the prediction of the UQAM. In case of UQAM, the Neutron Mass Quadratic Equationis changed to Neutron Mass Polynomial EquationNMPE, because it is non-quadratic. Second method for nd ∗ ∗ Z≥93, uses the 2 power of TVNM with ( A);NM -A graph; to generate NM which lead to the prediction of the UQAM for Z=94-107.The first method has short range limit or extension in estimation of UQAM with a little bit lower RMS. The second method has long range limit or extension in estimation of UQAM a little bit higher RMS. The UQAM of the elements Z=1-107 have been calculated. Thecalculated QAMfor 1230 isotopes belong to Z=81-99 from GNM valuesresult in the positive difference in alpha energies between two sequential even-even and odd-odd mass number A (i.e. ∆α (ee,oo) )andeven-odd and odd-even mass number A (i.e. ∆α (eo,oe) ) for each element. The calculated QAM values give the proper sequential values for β-, β+, α-decay energies without deviation and discontinuities. Only the quantized atomic masses QAM can give the positive values for ∆α (ee,oo) and ∆α (eo,oe) which should be started from Z=1 up to Z=200. These positive values have been calculated for more than 7900 isotopes belong to Z=1-118. With help from these positive values, NMT succeeded in calculation of the QAM of more than 8100 isotopes belong to period-8, Z=119-172, and Z=173-200 of period-9 that they will be submitted in the subsequent articles. NMT also succeeded in finding out the Island of the Stability. In the present article, we discussed the QAM of the isotopes of the elements Z=81-99. The UQAM are very close to the IAEA. The QAM of some neutron poor or rich can be calculated from the isobaric equation ISQMF. Although NMT has its powerful NMQE and IQMF to calculate the QAM for any isotope to any existent element but some time it uses its ISQMF to re-evaluate some disputed QAM for double checking. The Q-values of β-, β+, EC, α-decay energies have been calculated. IAEA showed in their website that Tl , Tl , Rn , Ac , Pa , U, Np , Np , Np , Am , Am , Cm , Bk , Bk , Cf , Es , Es , Es , and Es undergo EC, but SEFN calculations showed they cannot decay via EC.

227 Bahjat R. J. Muhyedeen

3. Results and Discussion The Quantized and Unquantized Atomic Masses (QAM and UQAM)- NMT- 2015 Version 3, of Z=81-99 Figures and Tables are in the Appendix-1. The polynomial equations, of the 2 nd power, were used to generate the quantized atomic masses QAM. The mass formula has RMS 0.72 MeV for quantized atomic masses QAM at stable nuclei and 2.80 MeV at far neutron poor and rich. Actually, the values of RMS of QAM does not reflect the accuracy of the calculated QAM values rather than they show the discrepancies with IAEA values. The polynomial equations, of the 3 rd up to 6 th power, were used to generate the unquantized atomic masses UQAM with RMS of 0.24 MeV. The UQAM of the elements Z=81-99 have been calculated and listed in Table-21. Another method was used for calculation the UQAM of the elements Z=81-99 using total variable neutron mass TVNM as explained in item 2.1 nd ∗ (which uses the polynomial equation of the 2 power of NM -A graph). Table-22 lists the values of the UQAM which calculated by TVNM and compared with literature values of DZ, WAW and Moller.The UQAM are very close to the IAEA. The NMT values of the proton S p and neutron S n separation energies are plotted in the Figures 21-23. The NMT QAM give a smooth curve for vs N while IAEA and WAW’ Eα show curling curves (see Fig. 24-26). The smooth and straight curves of confirm the mass quantization concept. The UQAM, Moller and IAEA failed to give the positive values for the two terms ∆α (ee,oo) and α (eo,oe) .

1. Thallium The thallium element has 21 even isotopes and 21 odd isotopes from IAEA 176 Tl-217 Tl. They were used as reference points RP in the polynomial of Neutron Mass Quadratic Equation NMQE (see Fig. 1A). Most of RP values showed deviation in the polynomial of even and odd isotopes, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 1B). Table-1 shows the difference between beta energies of IAEA and NMT. NMT added 16 new neutron poor NP isotopes 160 Tl-175Tl and 14 new neutron rich NR isotopes 218 Tl-233 Tl to the literature. All the calculated atomic masses of thallium are unquantized because they failed to give proper violet and blue values (see item 2.2). The RMS in calculation of the QAM is 6.0 MeV for all isotopes and 0.5546 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.47 MeV for all isotopes.

2. Lead The lead element has 22 even isotopes and 21 odd isotopes from IAEA 178 Pb-220 Pb. They were used as reference points RP in NMQE (see Fig. 2A). Most of RP values showed deviation in the polynomial of even and odd isotopes, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 2B). Table-2 shows the difference between beta energies of IAEA and NMT. NMT added 16 new neutron poor NP isotopes 162 Pb-177 Pb and 15 new neutron rich NR isotopes 221 Pb-235 Pb to the literature. All the calculated atomic masses of thallium are unquantized because they failed to give proper violet and blue values (see item 2.2). The RMS in calculation of the QAM is 7.4 MeV for all isotopes and 1.144 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.54 MeV for all isotopes.

3. Bismuth The bismuth element has 20 even isotopes and 20 odd isotopes from IAEA 184 Bi-221 Bi, 223 Bi-224 Bi. They were used as reference points RP in the NMQE (see Fig. 3A). Most of RP values showed deviation in the polynomial of even and odd isotopes, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 3B). Table-3 shows the difference between beta energies of IAEA and NMT. NMT added 16 new neutron poor NP isotopes 168 Bi-183 Biand 15 new neutron rich NR isotopes 222 Bi, 225 Bi-239 Bi to the literature. All the calculated atomic masses of thallium are unquantized because they failed to give proper violet and blue values (see item 2.2). The The Quantized Atomic Masses of the Elements: Part-5; Z=81-99 (Tl-Es) 228

RMS in calculation of the QAM is 8.45 MeV for all isotopes and 0.26 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.66 MeV for all isotopes.

4. Polonium The polonium element has 21 even isotopes and 21 odd isotopes from IAEA 186 Po-227 Po. They were used as reference points RP in the NMQE (see Fig. 4A). Most of RP values showed deviation in the polynomial of even and odd isotopes, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 4B). Table-4 shows the difference between beta energies of IAEA and NMT. NMT added 12 new neutron poor NP isotopes 174 Po-185 Po and 12 new neutron rich NR isotopes 228 Po-239 Po to the literature. All the calculated atomic masses of polonium are QAM. The RMS in calculation of the QAM is 7.133 MeV for all isotopes and 0.62 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.56 MeV for all isotopes.

5. Astatine The astatine element has 19 even isotopes and 20 odd isotopes from IAEA 191 At -229 At. They were used as reference points RP in the NMQE (see Fig. 5A). Most of RP values showed deviation in the polynomial of even and odd isotopes, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 5B). Table-5 shows the difference between beta energies of IAEA and NMT. NMT added 11 new neutron poor NP isotopes 180 At-190 Atand 14 new neutron rich NR isotopes 230 At-243 At to the literature. All the calculated atomic masses of astatine are QAM. The RMS in calculation of the QAM is 6.4 MeV for all isotopes and 0.01 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.42 MeV for all isotopes.

6. Radon The radon element has 18 even isotopes and 18 odd isotopes from IAEA 194 Rn-229 Rn. They were used as reference points RP in the NMQE (see Fig. 6A). Most of RP values showed deviation in the polynomial of even and odd isotopes, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 6B). Table-6 shows the difference between beta energies of IAEA and NMT. NMT added 12 new neutron poor NP isotopes 182 Rn-193 Rn and 14 new neutron rich NR isotopes 230 Rn-243 Rn to the literature. All the calculated atomic masses of radon are QAM. The RMS in calculation of the QAM is 5.033 MeV for all isotopes and 3.8 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.34 MeV for all isotopes.

7. Francium The francium element has 18 even isotopes and 19 odd isotopes from IAEA 197 Fr-233 Fr. They were used as reference points RP in the NMQE (see Fig. 7A). Most of RP values showed deviation in the polynomial of even and odd isotopes, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 7B). Table-7 shows the difference between beta energies of IAEA and NMT. NMT added 9 new neutron poor NP isotopes 188 Fr-196 Fr and 12 new neutron rich NR isotopes 234 Fr-245 Fr to the literature. All the calculated atomic masses of franciumare QAM. The RMS in calculation of the QAM is 3.2 MeV for all isotopes and 2.8 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.36 MeV for all isotopes.

8. Radium The radium element has 17 even isotopes and 17 odd isotopes from IAEA 201 Ra-234 Ra. The 15 isotopes were used as reference points RP in the NMQE (see Fig. 8A). Most of RP values showed a deviation in the polynomial of even and odd isotopes, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 8B). Table-8 shows the difference between beta energies of IAEA and NMT. NMT added 11 new neutron poor NP isotopes 190 Ra-200 Ra and 13 new neutron rich NR isotopes 235 Ra-247 Ra to the literature. All the calculated atomic masses of radium are QAM. The

229 Bahjat R. J. Muhyedeen

RMS in calculation of the QAM is 2.14 MeV for all isotopes and 0.07 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.32 MeV for all isotopes.

9. Actinium The actinium element has 16 even isotopes and 16 odd isotopes from IAEA 205 Ac-236 Ac. They were used as reference points RP in the NMQE (see Fig. 9A). Most of RP values showed a deviation in the polynomial of even and odd isotopes, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 9B). Table-9 shows the difference between beta energies of IAEA and NMT. NMT added 11 new neutron poor NP isotopes 194 Ac-204 Ac and 13 new neutron rich NR isotopes 237 Ac-249 Ac to the literature. All the calculated atomic masses of actinium are QAM. The RMS in calculation of the QAM is 1.62 MeV for all isotopes and 0.198 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.345 MeV for all isotopes.

10. Thorium The thorium element has 16 even isotopes and 15 odd isotopes from IAEA 208 Th-238 Th. They were used as reference points RP in the NMQE (see Fig. 10A). Most of RP values showed high deviation in the polynomial of even and odd isotopes, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 10B). Table-10 shows the difference between beta energies of IAEA and NMT. NMT added 12 new neutron poor NP isotopes 196 Th-207 Th and 13 new neutron rich NR isotopes 239 Th-251 Th to the literature. All the calculated atomic masses of thorium are QAM. The RMS in calculation of the QAM is 1.43 MeV for all isotopes and 0.95 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.22 MeV for all isotopes.

11. Protactinium The protactinium element has 14 even isotopes and 15 odd isotopes from IAEA 211 Pa-239 Pa. They were used as reference points RP in the NMQE (see Fig. 11A). NMT generated the GNM after several modifications to the DNM (see Fig. 11B). Table-11 shows the difference between beta energies of IAEA and NMT. NMT added 11 new neutron poor NP isotopes 200 Pa-210 Pa and 14 new neutron rich NR isotopes 240 Pa-253 Pa to the literature. All the calculated atomic masses of protactinium are QAM. The RMS in calculation of the QAM is 1.314 MeV for all isotopes and 0.11 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.19 MeV for all isotopes.

12. Uranium The uranium element has 12 even isotopes and 14 odd isotopes from IAEA 217 U-219 U, 221 U-243 U. They were used as reference points RP in the NMQE (see Fig. 12A). Most of RP values showed a deviation in the polynomial of even and odd isotopes and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 12B). Table-12 shows the difference between beta energies of IAEA and NMT. NMT added 16 new neutron poor NP isotopes 202 U-216 U, 220 U and 14 new neutron rich NR isotopes 244 U-257 U to the literature. All the calculated atomic masses of uranium are QAM. The RMS in calculation of the QAM is 1.3 MeV for all isotopes and 0.75 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.06 MeV for all isotopes.

13. Neptunium The neptunium element has 10 even isotopes and 10 odd isotopes from IAEA 225Np-244 Np. They were used as reference points RP in the NMQE (see Fig. 13A). Most of RP values showed high deviation in the polynomial of even and odd isotopes and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 13B). Table-13 shows the difference between beta energies of IAEA and NMT. NMT added 21 new neutron poor NP isotopes 204 Np-224 Np and 15 new neutron rich NR isotopes 245 Np-259 Np to the literature. All the calculated atomic masses of neptunium are QAM. The RMS in calculation of the QAM is 1.38 MeV for all isotopes and 0.45 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.048 MeV for all isotopes. The Quantized Atomic Masses of the Elements: Part-5; Z=81-99 (Tl-Es) 230

14. Plutonium The plutonium element has 10 even isotopes and 10 odd isotopes from IAEA 228 Pu-247 Pu. They were used as reference points RP in the NMQE (see Fig. 14A). Most of RP values showed high deviation in the polynomial of even and odd isotopes and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 14B). Table-14 shows the difference between beta energies of IAEA and NMT. NMT added 16 new neutron poor NP isotopes 212 Pu-227 Pu and 14 new neutron rich NR isotopes 248 Pu-261 Pu to the literature. All the calculated atomic masses of plutonium are QAM. The RMS in calculation of the QAM is 0.85 MeV for all isotopes and 1.18 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.04 MeV for all isotopes.

15. Americium The americium element has 10 even isotopes and 9 odd isotopes from IAEA 229 Am-230 Am,232 Am- 248 Am. They were used as reference points RP in the NMQE (see Fig. 15A). Most of RP values showed high deviation in the polynomial of even and odd isotopes and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 15B). Table-15 shows the difference between beta energies of IAEA and NMT. NMT added 15 new neutron poor NP isotopes 214 Am-228 Am, 231 Am and 15 new neutron rich NR isotopes 249 Am-263 Am to the literature. All the calculated atomic masses of americium are QAM. The RMS in calculation of the QAM is 0.75 MeV for all isotopes and 0.33 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.04 MeV for all isotopes.

16. Curium The curium element has 10 even isotopes and 10 odd isotopes from IAEA 233 Cu-252 Cu. They were used as reference points RP in the NMQE (see Fig. 17A). Most of RP values showed high deviation in the polynomial of even and odd isotopes and both curves give DNM.NMT generated the GNM after several modifications to the DNM (see Fig. 17B). Table-17 shows the difference between beta energies of IAEA and NMT. NMT added 17 new neutron poor NP isotopes 216 Cu-232 Cu and 15 new neutron rich NR isotopes 253 Cu-267 Cu to the literature. All the calculated atomic masses of curium are QAM. The RMS in calculation of the QAM is 0.3 MeV for all isotopes and 0.103 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.08 MeV for all isotopes.

17. Berkelium The berkelium element has 9 even isotopes and 9 odd isotopes from IAEA 233 Bk-234 Bk, 238 Bk-253 Bk. They were used as reference points RP in the NMQE (see Fig. 18A). Most of RP values showed high deviation in the polynomial of even and odd isotopes and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 18B). Table-18 shows the difference between beta energies of IAEA and NMT. NMT added 18 new neutron poor NP isotopes 218 Bk-232 Bk, 235 Bk- 237 Bk and 16 new neutron rich NR isotopes 254 Bk-269 Bk to the literature. All the calculated atomic masses of berkelium are QAM. The RMS in calculation of the QAM is 0.26 MeV for all isotopes and 0.20 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.044 MeV for all isotopes.

18. Californium The californium element has 10 even isotopes and 10 odd isotopes from IAEA 237 Cf-256 Cf. They were used as reference points RP in the NMQE (see Fig. 18A). Most of RP values showed high deviation in the polynomial of even and odd isotopes and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 18B). Table-18 shows the difference between beta energies of IAEA and NMT. NMT added 15 new neutron poor NP isotopes 222 Cf-236 Cf and 15 new neutron rich NR isotopes 257 Cf-271 Cf to the literature. All the calculated atomic masses of californium are QAM. The RMS in calculation of the QAM is 0.34 MeV for all isotopes and 0.22 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.04 MeV for all isotopes.

231 Bahjat R. J. Muhyedeen

19. Einsteinium The einsteinium element has 8 even isotopes and 9 odd isotopes from IAEA 241 Es-257 Es. They were used as reference points RP in the NMQE (see Fig. 19A). Most of RP values showed high deviation in the polynomial of even and odd isotopes and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 19B). Table-19 shows the difference between beta energies of IAEA and NMT. NMT added 17 new neutron poor NP isotopes 224 Es - 240 Es and 16 new neutron rich NR isotopes 258 Es-273 Es to the literature. All the calculated atomic masses of einsteinium are QAM. The RMS in calculation of the QAM is 0.42 MeV for all isotopes and 0.05 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.41 MeV for all isotopes.

4. Conclusion The novel theory NMT examined all experimental and theoretical atomic masses values of IAEA, JAEA, WAW, Moller and DZ which failed to give positive incremental difference in alpha energies between two sequential even-even and odd-odd mass number A; ∆α (ee ,oo) and two sequential even- odd and odd-even mass number A; ∆α (eo ,oe) .NMT called these values as unquantized atomic massesUQAM. NMT calculation proved that the prediction of the nuclear theoretical models for magic and doubly magic numbers for Z>82 were incorrect due to their reliance on the UQAM of IAEA and WAW. In present work, the QAM’s are calculated from the isotopic quantized mass formula IQMF of 2nd power and the UQAM’s are calculated from the isotopic quantized mass formula IQMF of 3 rd to 6 th power. The discrepancy (RMS) of the mass model is less than 335 keV for UQAM and 884 keV for QAM for the entire region of ground-state masses of 3160 nuclei ranging from 1H to 118 Og. The quantized atomic masses of 14500 nuclei ranging from Z=1 to Z=200 have been calculated, 1230 nuclides of them belong to Z=81-99(Tl-Es). These new atomic masses will be submitted in the forthcoming articles. The QAM of some neutron poor or rich can be calculated from the isobaric equation ISQMF. Although NMT has its powerful NMQE and IQMF to calculate the QAM for any isotope to any existent element but some time it uses its ISQMF to reevaluate some disputed QAM for double checking. The Q-values of β-, β+, EC, α-decay energies have been calculated through three different nuclear methods; SMT whichbased on mass defect MD (in proton and neutron mass), NMT which based on neutron mass defect NMD ( in neutron mass only), and SEFN (standard energy of formation of nuclide E ). SEFN calculations showed the Tl , Tl , Rn , Ac , Pa , U, Np , Np , Np , Am , Am , Cm , Bk , Bk , Cf , Es , Es , Es , and Es cannot undergo EC-decay. NMT not only succeeded in evaluation of the quantized atomic masses but also it found out several proton and neutron magic numbers in 2012 [ 54] such 6,14, 16 and 34 which are identical to the literature [ 59-61].

Acknowledgement A great thanks to NajahNooriAlshams and Hedeer Jawad Alshams for their huge work in collecting data from international nuclear websites, compiling nuclear data, managing excel and word files to prepare a hundred of tables, graphs and figures for the element Z-1-200.

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Appendix-1 See the flowing link https://www.researchgate.net/publication/319260876_The_Quantized_Atomic_Masses_of_the_Elemen ts_Part-5_Z81-99_Tl-Es