The alpha-cluster bands in 94Mo

Abstract

The 94 Mo nucleus is treated as an α-cluster interacting with an inert core through a phenomenological local potential. The properties of the ground state band of the α+ 90 Zr system, such as the energy levels, intercluster rms radii and B(E2) transition strengths were calculated. These results are compared with previous references and available experimental data. Some predictions were made concerning the negative parity band and the excited positive parity band.The α-cluster structure is an important feature for light nuclei. The α-cluster model has been successful in reproducing the behaviour of the energy spacings, electromagnetic properties, α-widths and α-nucleus elastic scattering data around the double shell closures such as . The search for α-cluster states in heavier nuclei is the natural sequence of investigations. Recent studies [4][5][6] indicate the persistence of α clustering in the A = 90 mass region.According to the α-cluster model, the total nucleus is viewed as an α-particle orbiting an inert core. In the case where both constituents have spin zero, no complications arise from the spin-orbit coupling. The 90 Zr medium-heavy nucleus presents a closed shell for neutrons and filled subshells for protons up to 2p 1/2 and may be considered approximately as an inert core. In this way the proposed model is employed to the 94 Mo nucleus, which is regarded as an α+ 90 Zr system. The interaction was described through a local phenomenological potential V (r) = V C (r) + V N (r) containing the nuclear and Coulomb terms. The Coulomb potential V C (r) is taken to be that of a point α-particle interacting with an uniformly charged spherical core of radius R = 5.793 fm. The intercluster nuclear potential The α-90 Zr system can be solved numerically to obtain the properties of the bound, quasibound and resonant states. The energy eigenvalues yield the levels of the spectrum and the associated wave functions are used to calculate other nuclear properties. The nucleons of the α-cluster must lie in shellmodel orbitals above those already occupied by the core nucleons, according to the Pauli principle. This restriction is defined by the quantum numberwhere N is the number of internal nodes in the radial wave function and L is the orbital angular momentum. G is a global quantum number which identifies a band of levels. In the case of the α-90 Zr system we have G ≥ 16, where G = 16 corresponds to the ground state band. This value is obtained from the Wildermuth condition [7] and yields an appropriate description of the α-90 Zr ground state band [4,5]. The energy levels of the ground state band (Fig. 1) and the respective radial wave functions were obtained solving directly the Schrödinger equation for the system. These functions were used to determine the associated B(E2) transition rates and the intercluster rms radii for this band (Table I). The calculated ground state band shows a quasirotational spectrum and it is in total agreement with the theoretical values of Ref. [4], where the spectrum is obtained by using ...

α-cluster structure in even-even nuclei aroundMo94

“…Because of the enhanced value of Vo, the bandheads of the theoretical negative parity bands lie close to Ex = 1 MeV, which differs from previous predictions for 94Mo [12,14,17]. According to the criterion adopted to select the experimental levels, there are no experimental 1" and 3" states for compar ison with the calculated bands (see Fig.…”

“…The work of Ohkubo [12] analyzes the same structure in 94Mo through a double folding potential; in this case, a good description of the a + 90Zr elastic scattering data is obtained, the 94Mo ground state band is reproduced with a weak dependence on the quantum number L, and the absolute values of the B{E2) transition rates are well described with a small effective charge (8e = 0.2e). Following works of Michel et al [13] and Souza and Miyake [14] reinforce the indications on the a-cluster structure in the 94Mo states. Concerning 2l2Po, the results obtained in Refs.…”

“…Previous works [12,14,17] discuss the existence of an a + core negative parity band for 94Mo and indicate that the 1 ~ bandhead should lie at Ex = 6-7 MeV, however, such predictions are not compared with experimental energies of 94Mo. Therefore, at this stage, any calculation concerning the negative parity bands of the studied nuclei should be inter preted as a theoretical prediction that lacks complementary experimental information.…”

Search for the $α$ + core structure in the ground state bands of $22 \leq Z \leq 42$ even-even nuclei

“…shape; in that work, an exploratory calculation of the negative parity bands was made for 92 Zr, 94 Mo, 96 Ru, and 98 Pd, where a depth V 0 = 238 MeV was employed to give a satisfactory reproduction of the incomplete experimental negative parity bands, while V 0 = 220 MeV was applied to the ground state bands. Using the α + core potential of the present work with the fixed depth V 0 = 220 MeV, the 1 − bandheads for 92 Zr (G = 15) and 94 Mo (G = 17) are found at E x = 7.514 MeV and 7.084 MeV, respectively; the E x (1 − ) value mentioned for 94 Mo is similar to other predictions on the G = 17 band[7,14,79]. However, the calculated E x (1 − ) values with V 0 = 220 MeV are above the experimental bands considered in Ref [12]…”

ALPHA CLUSTERING AND WEAK COUPLING IN THE 93Nb REGION

“…On the other hand, from the viewpoint of a unified description of bound and scattering for the α+ 90 Zr system, the present author suggested that the α cluster model is still successful in understanding the structure of 94 Mo. 11 The structure of 94 Mo is also described in the α+ 90 Zr cluster model using a phenomenological potential [12][13][14][15] and a double folding model potential. 13 Although there are not many experimental data of α transfer reactions in this region compared with the 20 Ne and 44 Ti regions, there are some indications which suggest the importance of α clustering in this mass region.…”