Spectroscopic study of the N = 27 nuclei by means of the (τ, α) reaction

The (τ, α) reaction on ⁴⁸Ca, ⁵⁰Ti, ⁵²Cr and ⁵⁴Fe target nuclei has been studied at 25 MeV incident energy. Angular distributions have been measured from 5° to 40° with a split-pole spectrometer in a large range of excitation energy. A local zero-range DWBA analysis has been carried out, using an isospin-dependent potential for the calculation of the neutron form factor, in order to get a coherent set of spectroscopic factors for both T_> and T_< levels in different nuclei. Assignments of l-values have been done for a large number of levels, most of them previously unknown, and energy centroids of hole states have been determined. Spectroscopic factors in ³⁹Ca, ⁴⁷Ti, ^{49, 52, 53}Cr have also been obtained for strongly excited states. A sum rule analysis has been carried out for the N = 27 nuclei: the $\text{1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{T}{}_{\mathrm{<}}$ hole strengths are generally fully exhausted by the observed levels, whereas only a fraction of the $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ strength has been evidenced. The $\text{1}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{, 1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ analog states have been observed in all nuclei; in ⁵³Fe, the $\text{1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ analog states appear to be split in several components. In addition, a CRC analysis has been carried out for some levels with angular distributions not accounted for by a direct pick-up process. These levels are tentatively identified with states resulting from the coupling of one $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ neutron hole with excited states of the target nucleus. In particular, the $\text{5}\text{2}{}^{\mathrm{?}}\text{and}\text{9}\text{2}{}^{\mathrm{?}}$ members of the $\text{[2}{}^{\mathrm{+}}\text{?}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{]}$ configuration have been identified in each final nucleus. Unambiguous J^π assignments are made; and the two-step (τ, α) reaction therefo e appears as a useful spectroscopic tool, especially for investigating high spin states.