European Journal of Scientific Research ISSN 1450-216X / 1450-202X Vol. 148 No 2 January, 2018, pp. 201-233 http://www. europeanjournalofscientificresearch.com The Quantized Atomic Masses of the Elements: Part-5; Z=81-99 (Tl-Es) 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 QAM-UQAM-NMT-2015-Ver-3. 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, super- heavy 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 period-9, Z=173-200 ). 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 MΜ/ N MΜinside 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 MΜ 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 MΜ (i.e. M A=ZM H+N MΜ) after manipulation far ∗ from B.E formula. In this manner, the corrected single variable neutron mass MΜwill 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 MΜ. 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 MΜ in the stable nuclei, which are called quantized QNM andunstablevariable masses ∗ MΜin 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 MΜ values and nominates the MΜ 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 MΜ-ln( A) graph with poor R values ((R <0.9999) and consonant neutron mass CNM (i.e.