On the transitions between seniority-four and seniority-two states compared to the two-phonon-one-phonon transitions

doi:10.1016/0375-9474(68)90822-1

Nuclear Physics A

Volume 114, Issue 1, 17 June 1968, Pages 161-183

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Abstract

Using the generalized quasi-spin representation, sum rules are derived for the electric quadrupole transition rates connecting the first 2⁺ state of seniority two and states of various seniority (v = 2 → v = 4). It is shown that the sums over states of seniority four approach the vibrational sum rule for large degeneracies. In several cases, individual transitions have been calculated for a surface delta interaction. When the single-particle states are degenerate, it is shown that 0⁺, one 2⁺ and one 4⁺ exhaust almost entirely v = 2 → v = 4 sum rule. A calculation is also performed of these transitions in a case where the single-particle energies are no longer degenerate. Here there is some mixing between seniority-2 and -4 states, and the picture concerning transition rates is more complicated.

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Cited by (3)

On the transition from shell structure to collective behavior. A simplified shell-model study
1972, Nuclear Physics, Section A
To study the feasibility of carrying out shell-model calculations in nuclei with active protons and neutrons in different major shells, the following simple idealized model has been studied: (i) Proton and neutron configurations are chosen to be $(f_{52} p_{32} p_{12})^{n}_{p}$ and $(g_{72} d_{52} d_{32} s_{12})^{n}_{n}$ , so that results for the separate proton and neutron basis states to be used in any approximation scheme can be compared with the results for exact shell-model calculations, (ii) The proton and neutron single-particle energies for these active shells are separately taken to be degenerate. (iii) The two-body interaction is approximated by the simple surface delta interaction (SDI). To effect the severe truncation of the full shell-model space needed to make such a shell-model study possible the separate proton and neutron parts of the shell-model basis are built from a superposition of the favored pair states of the SDI (with J ≠ 0, as well as J = 0). In the neutron configuration $(g_{72} d_{52} d_{32} s_{12})^{n}_{n} = 4$ , for example only three of the 94 shell-model states with J_n = 2 are retained in the truncation scheme. In this highly truncated basis both the energies and the strong B(Ek) values for the transitions from these states to similar favored states with other J-values are within a few percent (or better) of the results of exact shell-model calculations. A truncation of the shell-model space based on such superpositions of favored pair states leads to a manageable shell-model basis (dimensions ≦ 200). (a) The number of states in the separate proton and neutron parts of the basis are small enough (8–13 for the proton space, 15–30 for the neutron space). They are also the key states in the following sense (b) They include the low-lying energy eigenstates of the separate p-p and n-n parts of the interaction (c) They contain most of the collective coherence of the separate proton and neutron configurations. (d) The matrix elements of the n-p part of the interaction between the favored states are in general very large compared with the matrix elements between a favored and an excluded state. The latter effect is studied from several aspects, in particular in terms of sum rules for the matrix elements of the surface multipole operators from which the n-p part of the SDI is built. For most of the low-lying favored states the sum over all favored states gives more than 90 % of the total sum rule for the squares of matrix elements of the surface multipole operators. The results of shell-model calculations in this truncation scheme, with n_p = 4 or 6, and n_n = 4, show many of the features of a quadrupole vibrational spectrum. The presence and exact nature of a 0⁺ member of the 0⁺, 2⁺, 4⁺ “two-phonon triplet” is dependent on the inclusion of the key favored states with seniorities of 6.
Analysis of the properties of the odd-mass single closed shell nuclei with a surface delta interaction
1970, Nuclear Physics, Section A
The surface delta interaction has been applied in a calculation of the odd-mass isotopes of Ni and Pb and of the nucleus ²¹¹At. Exact shell-model calculations have been performed in all cases except for lead isotopes containing more than three holes (²⁰³Pb-¹⁹⁷Pb). The Bogoliubov-Valatin method combined with the Tamm-Dancoff approximation in the subset of one-and three-quasiparticle configurations has also been used. The comparison between the results obtained in those two ways shows that the quasiparticle method works rather well. The agreement with experiment is quite good in general and is comparable with that achieved with more complicated interactions. The exact wave functions have been analysed in terms of the coupling of a particle or a hole to the ground state of the neighbouring nuclei with only two particles or holes outside closed shells. Finally the theoretical spectroscopic factors of the reactions ⁵⁸Ni(d, p) ⁵⁹Ni, ²⁰⁶Pb (d, t) ²⁰⁵Pb and ²⁰⁶Pb (p, d) ²⁰⁵Pb have been studied in connection with this analysis and compared with the experimental results and calculations by other authors.
Interacting boson model with surface delta interaction between nucleons
1985, Physical Review C

^☆: Work partially supported by the National Science Foundation.

^††: Address postale, BP. No. 1, 91 Orsay.

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Nuclear Physics A

On the transitions between seniority-four and seniority-two states compared to the two-phonon-one-phonon transitions☆

Abstract

Revs. Mod. Phys.

Compt. Rend.

Compt. Rend.

Progr. Theor. Phys.

Phys. Rev.

Mat. Fys. Medd. Dan. Vid. Selsk.

Revs. Mod. Phys.

Phys. Lett.

Nucl. Phys.

Nucl. Phys.

Phys. Rev.

Phys. Rev.

Phys. Rev.

On the transition from shell structure to collective behavior. A simplified shell-model study

Analysis of the properties of the odd-mass single closed shell nuclei with a surface delta interaction

Interacting boson model with surface delta interaction between nucleons