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Nuclear Spins and Moments of the Actinides

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Nuclear Spins and Moments of the Actinides APPENDIX I NUCLEAR SPINS AND MOMENTS OF THE ACTINIDES Nuclear spins and nuclear moments are used to test the single‐particle models and nuclear quadrupole moments provide the deformation of the nucleus. In the following table, we present measured values of ground state spin in units of h, magnetic dipole moment (m) in units of nuclear magneton, and spectroscopic quadrupole moment (Q) in units of barns. The data have been taken from Raghavan (1989) and Firestone and Shirley (1996). Nuclear Nuclear magnetic moment Electric quadrupole Nuclide spin (ħ) (nuclear magneton) moment (barns) 217Ac 9/2 þ3.825(45) 227Ac 3/2 þ1.1(1) þ1.7(2) 229Th 5/2 þ0.46(4) þ4.3(9) 228Pa 3 þ3.48(33) 230Pa 2 þ2.00(29) 231Pa 3/2 þ2.01(2) –1.72(5) 233Pa 3/2 þ3.39(70) À3.0 233U 5/2 0.59(5) 3.663(8) 235U 7/2 À0.38(3) 4.936(6) 237Np 5/2 þ3.14(4) þ3.886(6) 238Np 2 239Np 5/2 239Pu 1/2 þ0.203(4) 241Pu 5/2 À0.683(15) þ5.6(20) 241Am 5/2 þ1.61(3) þ4.2(13) 242Am 1 þ0.3879(15) À2.4(7) 242mAm 5 þ1.00(5) þ6.5(20) 243Am 5/2 þ1.61(4) þ4.30(3) 243Cm 5/2 0.41 245Cm 7/2 0.5 (1) 247Cm 9/2 0.37 249Bk 7/2 2.0(4) þ5.79 249Cf 9/2 À0.28 253Es 7/2 þ4.10(7) 6.7(8) 254mEs 2 2.90(7) 3.7(5) Firestone, R.B. and Shirley, V.S. (eds.) (1996). Table of Isotopes, 8th edn. John Wiley, New York. Raghavan, P. (1989) At. Nucl. Data Tables, 42, 189–291. 3441 APPENDIX II NUCLEAR PROPERTIES OF ACTINIDE AND TRANSACTINIDE NUCLIDES Irshad Ahmad DISCUSSION In this appendix, an elementary discussion of the nuclear properties of heavy elements is presented. For a better understanding of the subject, the reader should refer to nuclear chemistry textbooks (Krane, 1988; Choppin et al., 2002) and for the information on decay data, the Table of Isotopes (Firestone and Shirley, 1996) or the Table of Radioactive Isotopes (Browne and Firestone, 1986) or Nuclear Data Sheets (Tuli, 2004) should be consulted. Isotopes of all elements with Z 89 are radioactive. The most common mode of decay for these nuclei is by the emission of alpha particles (4He ions). Alpha decay energies have been experimentally measured (Browne and Firestone, 1986; Firestone and Shirley, 1996) for most nuclides and these can also be calculated from atomic masses (Wapstra et al., 2003). The a decay of a nucleus with atomic number Z and atomic mass A produces a daughter nucleus with atomic number Z–2 and atomic mass A–4. During the a decay, about 2% of the available decay energy is imparted to the recoiling daughter nucleus and the remaining energy is carried off by the fast moving a‐particle. Several groups of a‐particles are emitted by a sample of a nuclide, each with a definite energy. For the actinide nuclides, a‐particle energies range from about 4 to 11 MeV. As a rule, a‐particle energy increases with increasing Z, and for a given element, it decreases with increasing mass number. The a‐decay half‐life decreases exponentially with increasing energy. As a guide, every 50 keV increase in the decay energy reduces the half‐life by a factor of 2. The dependence of the a‐decay half‐life on the decay energy is given by the well‐known Geiger–Nuttall law and more recently by Viola–Seaborg for- mula. A very useful quantity that facilitates the understanding of the mecha- nism of a‐decay is the concept of hindrance factor. It is defined as the ratio of the experimental partial a‐decay half‐life to the theoretical half‐life calculated on the assumption that the a‐particle pre‐exists in the nucleus and during its emission, it carries no angular momentum. An alpha transition in which the 3442 Nuclear properties of actinide and transactinide nuclides 3443 ground state configuration of the parent nucleus remains unchanged is called ‘favored transition’. All alpha transitions between the ground states of even– even nuclei are favored transitions and are assigned a hindrance factor of one. Like elements of lower Z, each actinide element has one or more b‐stable isotopes. Isotopes heavier than the b‐stable isotope decay by the emission of bÀ particles (electrons) and isotopes lighter than the b‐stable isotopes decay by electron capture (EC). Electron capture decay is usually accompanied by the emission of K x‐rays of the daughter nuclide. These x‐rays provide a signature of the decaying nuclide. In heavy nuclei, bþ/EC ratio is very small and, as a consequence, positron (bþ) emission has been observed only in a few nuclei. The b‐decay energy increases as the mass of the isotope gets further away from the line of b‐stability. A quantity denoted by log ft is very useful in classifying the b transitions and estimating the b‐decay half‐lives of unknown nuclei. The ft value, also called the reduced b transition probability, is the energy‐independent transition rate. Spontaneous fission is a decay process in which a nucleus breaks up into two almost equal fragments. Each fission event is accompanied by the release of about 200 MeV energy and the emission of two to four neutrons. More than hundred nuclides are produced in fission of a nuclide sample and the mass yields and charge distributions have been measured for many fissioning systems (Wahl, 1989; Ahmad and Phillips, 1995). The fission half‐life depends on the fissility parameter Z2/A and is the major decay mode for many isotopes of element 100 and beyond. Nuclides with reasonable fission branch and available 248 5 252 for experiments and industrial use are Cm (t1/2 ¼ 3.40 Â 10 years) and Cf 252 (t1/2 ¼ 2.64 years). The isotope Cf is widely used as a neutron source in industry and research. Another rare mode of decay for heavy elements is the decay by the emission of intermediate mass fragments. These fragments are heavier than a particles but smaller than fission fragments. The branching ratio for this kind of radio- activity is extremely small (10À10). Examples of such radioactivity are the 24Ne emission by 231Pa and 232U (Price, 1989). Alpha and b transitions usually populate excited states in addition to the ground states of the daughter nuclei. The excited states then decay to the ground state by emission of g rays and conversion electrons. Typical half‐lives of the excited states range from 10À9 to 10À14 s. However, in some cases, the decay of an excited state is forbidden for fast magnetic dipole (M1), electric dipole (E1), or electric quadrupole (E2) transitions because of the angular momentum selection rule. Such states have half‐lives between nanoseconds and years. An excited state that has a half‐life value greater than a nanosecond is called a ‘metastable’ state or ‘isomer’. The isomeric state either de‐excites to the ground state of the same nucleus by an internal transition (IT) or it decays by the usual mode of disintegration. Most isomers occur because of the large difference between the spins of the excited state and the ground state. However, there are isomers which result not 3444 Discussion by the difference in the spins of the states but by the difference in the shapes. These isomers decay by fission and are called ‘fission isomers’ or ‘shape isomers’ and have half‐lives between 10À9 and 10À3 s. These isomers have deformations that are twice as large as the deformations of the ground states. More than 50 fission isomers have been discovered (Vandenbosch, 1977). Very neutron‐deficient nuclides decay predominantly by electron capture (EC). In some of these nuclei, the EC decay energy is quite large (> 4 MeV) and hence states at high excitation energy are populated in the daughter nucleus and a small fraction of these excited states decay by fission. Delayed fission of many nuclei has been observed (Hall and Hoffman, 1992). Nuclear structure studies of actinide nuclides have been performed using a variety of techniques. These include high‐resolution alpha, electron and gamma‐ray spectroscopy, charged‐particle transfer reaction spectroscopy, and Coulomb excitation studies. These investigations have provided significant information on the shape, size, and single‐particle potential of actinide nuclei. The available data establish a spheroidal shape for nuclei with A 225, with major to minor axes ratio of 1.25. The intrinsic quadrupole moments of actinide nuclei have been measured to be about 10–23 ecm2 and the nuclear radii are about 10À12 cm. Although most actinide nuclei have spheroidal shapes, there are indications that some neutron‐deficient Ac and Pa nuclei have small octupole deformation in their ground states. These nuclei are pear‐shaped and are axially symmetric but they are reflection asymmetric. Examples of such nuclei are 229Pa and 225Ac (Ahmad and Butler, 1993). In nuclei, nucleons (neutrons and protons) move in orbits under the influence of the central nuclear potential. Nilsson (1955) and others (Chasman et al., 1977) have calculated the eigenvalues and eigenfunctions of nucleons in a deformed potential as a function of the deformation b. Plots of the eigenvalues versus the deformation, commonly known as Nilsson diagrams, are extremely useful in understanding the single‐particle properties of actinide nuclei. Each Nilsson state is characterized by a set of quantum numbers O p, N, Nz, and L. The quantum number O is the projection of the single‐particle angular momen- tum on the nuclear symmetry axis and p is the parity of the wavefunction.
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