Inelastic Scattering of 14.4-MeV Protons by the Even Isotopes of Titanium

Abstract

Elastic and inelastic scattering of 14.4-MeV protons from isotopically enriched targets of ^s.so'pi W ere studied. Angular distributions for many groups separated by more than 40 keV were obtained. The data were analyzed using the coupled-channel calculation. The vibrational collective model was used to describe the states of the bombarded nucleus. Several octupole states were found in both 46 Ti and 48 Ti but only one in 50 Ti. These results were compared with the results of a-particle scattering on the same nuclei. It was found that a discrepancy exists between the results of the experiments in the magnitudes of the deformabilities obtained for the octupole states. Spins and parities of some states in 48 Ti and 50 Ti were suggested. Electromagnetic transition rates were inferred from the deformabilities deduced from inelastic scattering data.

Local Homology and Cohomology, Homology Dimension and Generalized Manifolds

“…The corresponding neutron value from the VIBM is δ nn 2 = 0.924(±10%) fm. δ pp 2 values resulting from (p, p ) studies reported in the literature [4][5][6]8] scatter between ≈ 0.82 and 1.2 fm. Clearly, δ nn 2 < δ em 2 .…”

“…As a first step towards increased complexity, the VIBM derivation was repeated assuming a one-and two-phonon vibrational model, following the fitting procedures described in section 4. A similar approach has been taken in studies of proton scattering from titanium [4]. The 984 keV level was taken to be the one-phonon state.…”

“…If one increases β 2 to approximately 0.22 the one-and twophonon model will give inelastic-scattering results similar to those of the VIBM. Chargedparticle work has suggested octupole vibrations in 48 Ti at excitations above ≈ 3 MeV with β 3 ≈ 0.15-0.20 [4,7]. However, before one can justify the additional calculational complexity of including two-phonon and octupole levels in the neutron calculations the measured neutron data must be considerably improved.…”

“…Thus elemental titanium is reasonably represented by an even-even f 7/2 collective nucleus with a yrast 2 + level at approximately one MeV. The even titanium isotopes are in a region where the yrast 2 + levels are classic vibrators [3], and charged-particle studies indicate a strong quadrupole vibrational interaction [4][5][6][7][8][9][10]. In addition, octupole states have been reported above excitations of ≈ 3 MeV.…”

High-spin states in48Ti

“…The situation has recently been reviewed by Signorini et al [1]. Experimental investigations prior to this work were concerned with low-spin states I- [4][5][6][7][8][9][10][11][12][13][14][15][16] and have in addition yielded candidates for the J~=8 + and 10 § yrast states [17]. Such calculations have been performed as early as 1964 by McCullen, Bayman and Zamick [2].…”