Collective motion in the nuclear shell model. I. Classification schemes for states of mixed configurations

To understand how collective motion can develop in the shell-model framework it is necessary to study configuration interaction. With this in mind, group-theoretical methods are used to investigate the possible classification schemes for a number of nucleons in m xed configurations. One particular coupling scheme, which is associated with the degeneracy of a harmonic oscillator potential and which, in a following paper, will be shown to have collective properties is described in detail. The wave functions in this scheme are seen to be very similar to those resulting from an actual shell-model calculation with configurational mixing.

Download Full-text

Collective motion in the nuclear shell model III. The calculation of spectra

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1963.0071 ◽

1963 ◽

Vol 272 (1351) ◽

pp. 557-577 ◽

Cited By ~ 133

Keyword(s):

Shell Model ◽

Collective Motion ◽

Mass Region ◽

Wave Functions ◽

Nuclear Shell Model ◽

Matrix Elements ◽

One Dimensional ◽

The One ◽

Nuclear Shell ◽

Main Pattern

A method is derived for calculating matrix elements of a two-body interaction in wave functions which were classified in part I interms of the group U 2- . For simplicity, a Cartesian basis of intrinsic functions is introduced in which the one-dimensional oscillators in x, y and z are separately diagonal. An application to 24 Mg in L-S coupling shows very little mixing of the quantum number K but an appreciable (10 to 20 %) mixing of U 3 representations (λμ). Overall agreement with experiment is quantitatively only tolerable but the main pattern of the spectrum is undoubtedly given by the lowest representation (84). On this basis, suggestions are made concerning the type of spectra to be expected for even and odd parity levels of the even-even nuclei in the mass region 16 < A < 40.

Download Full-text

Collective motion in the nuclear shell model IV. Odd-mass nuclei in the sd shell

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1968.0033 ◽

1968 ◽

Vol 302 (1471) ◽

pp. 509-528 ◽

Cited By ~ 23

Keyword(s):

Shell Model ◽

Effective Charge ◽

Collective Motion ◽

Energy Levels ◽

Electromagnetic Properties ◽

Coupling Scheme ◽

Nuclear Shell Model ◽

Nuclear Shell ◽

Shell Energy

The U 3 coupling scheme is used as the basis for a survey of the odd nuclei in the sd shell. Energy levels and electromagnetic properties are compared with experiment. In the first half of the shell, A < 28, there is agreement, but in the second half the data suggest something much closer to jj coupling. The need for an effective charge also disappears beyond A = 28.

Download Full-text

Nuclear energy levels in 58Ni

Tikrit Journal of Pure Science ◽

10.25130/j.v24i3.824 ◽

2019 ◽

Vol 24 (3) ◽

pp. 100

Author(s):

Firas Zuhair Majeed1 ◽

, Ammar A. Battawy2 ◽

Muhanned A. Ahmed2

Keyword(s):

Experimental Data ◽

Shell Model ◽

Energy Levels ◽

Nuclear Shell Model ◽

Harmonic Oscillator Potential ◽

Angular Momenta ◽

Inert Core ◽

Modified Surface ◽

Nuclear Shell ◽

Surface Delta Interaction

Energy levels, total angular momenta and parity for two nucleons that present outside closed core 56Ni (Nickel) which occupied FP nuclear shell have been calculated using nuclear shell model application. We have used FP M3YE interaction to calculate energy levels of 58Ni, in addition, the results are compared with experimental data, modified surface delta interaction (MSDI), Reid's potential (RP) and non-zero pairing shell model (NZPSM). Harmonic Oscillator potential is used to generate single particle wave functions in FP shell and considering as an inert core. Oxford Buenos Aires Shell Model (OXBASH) code for nuclear shell model calculation has been utilized to carry out the calculations and comparison with experimental data had been done. http://dx.doi.org/10.25130/tjps.24.2019.054

Download Full-text