Abstract
Inelastic longitudinal electron scattering form factors for secondexcited state C42 in 42Ti nucleus have been calculated using shellmodel theory. Fp shell model space with configuration (1f7/2 2p3/21f5/2 2p1/2) has been adopted in order to distribute the valenceparticles (protons and neutrons) outside an inert core 40Ca. Modernmodel space effective interactions like FPD6 and GXPF1 have beenused to generate model space vectors and harmonic oscillator wavefunction as a single particle wave function. Discarder space (coreorbits + higher orbits) has been included in (core polarization effect)as a first order correction in microscopic theory to measure theinterested multipole form factors via the model space.Gogny and Michigan sum of three-range Yukawapotential (M3Y-p2) have been utilized as a residual interaction tocouple the (particle-hole) pair across the model space active particlesand the excitation energy of the pair is (2ħω) and four options for theused effective and residual interactions were determined for thetransitions from (+0) to (+01,2,3), (+21,2,3) and (+41,2,3).
Highlights
The obtained information from the high energy of electron scattered by the nuclei depends on the magnitude of the de-Broglie wave length that is associated with the electron compared with the range of the nuclear forces
In the present work, 40Ca is used as inert core and the model space is the fp shell
The Titanium nucleus 42Ti is considered in the fp-shell region
Summary
The obtained information from the high energy of electron scattered by the nuclei depends on the magnitude of the de-Broglie wave length that is associated with the electron compared with the range of the nuclear forces. Inelastic electron scattering form factors for the 0+→2+ transitions in some even Ti isotopes were studied in terms of the projected Hartree-Fock Bogoliubov wave function in the 2p-1f shell resulting from a slightly modified version of the Kuo-Brown effective interaction [6]. Salman and Adeeb in 2013[12] studied the form factors for the inelastic electron scattering to 2+, 4+ states in 46,48,50Ti in the framework of shell model. They used MSDI as effective interaction and M3Y as residual interaction. R1(c) t1(SE) t1(TE) t1(SO) t1(TO) R2(c) t2(SE) t2(SO) t2(TE) t2(TO) R3(c) t3(SE) t3(SO) t3(TE) t3(TO) R1(LS) t1(LSE) t1(LSO) R2(LS) t2(LSE)
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