Ca⁴⁰ (α, α'): A test of particle-hole calculations☆

The experimental nuclear structure data and decay data are evaluated for the known nuclides of mass 40 (Mg, Al, Si, P, S, Cl, Ar, K, Ca, Sc, Ti). Detailed evaluated nuclear structure information is presented with the best values recommended for level energies, half-lives, γ-ray energies and intensities, decay properties (energies, intensities and placement of radiations), and other spectroscopic data. The ⁴⁰Ca and ⁴⁰K nuclides remain as the most extensively studied from many different reactions and decays; no excited states are known in ⁴⁰Mg, ⁴⁰Al, ⁴⁰P and ⁴⁰Ti. This work supersedes the earlier full evaluation of A=40 by J. Cameron and B. Singh (2004Ca38).

Nuclear spectroscopic information for the known nuclides of mass 40 (Al,Si,P,S,Cl,Ar,K,Ca,Sc,Ti) has been evaluated. The principal sources of the adopted levels presented are Endt's evaluations (1990En08, 1978En02). The data sets for reactions and decays, including all available gamma-ray data, are based mostly on the original literature. There are no data available for the excited states in ⁴⁰Al, ⁴⁰Si, ⁴⁰P and ⁴⁰Ti. The identification and particle stability of ⁴⁰Mg are still uncertain, although search for this nuclide has been made (2002Lu09,2002No11,2003Pe31).

Shape coexistence in doubly even nuclei is reviewed. Two main theoretical approaches are presented. The first is essentially the shell model with the excitation of pairs of protons and/or neutrons across closed shells or subshells together with a residual proton-neutron interaction. The second is the deformed mean-field approach. The first is broadly defined so that it includes various truncation schemes to the shell model including generalized seniority and the interacting boson model. The presentation of the theory has two main aims: to provide a framework into which the majority of theoretical studies of shape coexistence can be placed and to provide a framework within which a unified view can be discussed. Selected experimental data are shown from ¹⁶O to ²³⁸U. Our criteria for selection emphasize detailed spectroscopic evidence (“fingerprints”) for coexisting shapes.

The nucleus ⁷²Ge has been Coulomb excited using ¹⁶O, ⁵⁸Ni and ²⁰⁸Pb. Seventeen E2 matrix elements coupling the low-lying states have been determined. Based on these data, an interpretation of the structure of ⁷²Ge has been proposed that includes an “intruder” 0⁺ state perturbing what the present work shows to be a triaxial quadrupole-deformed collective rotational structure.

A comparison of the results of the ⁴⁰Ar(⁶Li, d)⁴⁴Ca reaction with previous results for ⁴²Ca(t, p)⁴⁴Ca is used to investigate core-excited 0⁺ states in ⁴⁴Ca.

The static quadrupole moments of the lowest 2⁺ states in ^{46, 50}Ti and ^{50, 52, 54}Cr were measured to be −21±6, 8±16, −36±7, −14±8 and −21±8e· fm² respectively. Values for B(E2;0₁⁺ → 2₁⁺) of 855±40, 315±30, 1020±40, 660±30 and 850±30 e² · fm⁴ were measured for ^{46, 50}Ti and ^{50, 52, 54}Cr respectively. Shell-model calculations for these and other $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ shell nuclei were compared to the data. The N = 26, 28 nuclei are adequately described by the shell model if one-particle excitation into the p_{$\text{3}\text{2}$} and f_{$\text{5}\text{2}$} shells is allowed, but the other nuclei appear to have a more complicated structure. The coexistence model which has been applied to the calcium isotopes is in qualitative agreement with the present results and the assumption that the deformed band moves to a higher excitation energy as N → 28.