[Paper Review] Level excitation and transition probabilities of some nuclei in the lower fp-shell

Fouad A. Majeed|arXiv (Cornell University)|Nov 30, 2005

Nuclear physics research studies3 citations

TL;DR

This study performs unrestricted shell model calculations in the lower fp-shell using OXBASH for 46Ti, 46Cr, and 46V, employing GXPF1, FPD6, and KB3G effective interactions. It finds excellent agreement with experimental level energies using FPD6, but GXPF1 provides superior agreement with experimental transition strengths B(E2), indicating its greater reliability for spectroscopic properties in this region.

ABSTRACT

Unrestricted shell model calculations in the lower $fp$-shell region for the nuclei $^{46}$Ti, $^{46}$Cr and $^{46}$V have been performed for the isovector T=1 positive parity states using the shell model code OXBASH for Windows by employing the effective interactions GXPF1, FPD6 and KB3G. The level schemes and transition strengths $B$($E$2;$\downarrow$) are compared with the recently available experimental data. A very good agreement were obtained for all nuclei.

Motivation & Objective

• To test the predictive power of modern effective interactions—GXPF1, FPD6, and KB3G—in describing nuclear structure in the lower fp-shell region.
• To compare theoretical level excitation energies and E2 transition probabilities with recent experimental data for 46Ti, 46Cr, and 46V.
• To assess the performance of different effective interactions in reproducing both level spectra and transition strengths, particularly focusing on isovector T=1 states.
• To evaluate the role of effective charges (eπ=0.7e, eν=0.5e) in accurately modeling E2 transition strengths within the harmonic oscillator basis.
• To determine which effective interaction—FPD6, GXPF1, or KB3G—best reproduces experimental data for both energy levels and transition probabilities in the studied nuclei.

Proposed method

• Conducted full-shell model calculations in the fp-model space (1p3/2, 1p1/2, 0f7/2, 0f5/2) outside a 40Ca core using the OXBASH for Windows code.
• Employed three effective interactions—GXPF1, FPD6, and KB3G—within the same model space to compute level spectra and E2 transition probabilities.
• Calculated B(E2; ↓) matrix elements assuming pure E2 transitions in the harmonic oscillator basis, with core polarization effects included via effective charges.
• Used proton effective charge eπ = 0.7e and neutron effective charge eν = 0.5e for transition strength calculations.
• Compared theoretical results with experimental data from the literature, including excitation energies and B(E2) values for ground-state bands.
• Analyzed the performance of each interaction across all three nuclei, focusing on both energy level agreement and transition strength reproduction.

Experimental results

Research questions

• RQ1 How well do the GXPF1, FPD6, and KB3G effective interactions reproduce the experimental excitation energies of 46Ti, 46Cr, and 46V in the lower fp-shell?
• RQ2 Which effective interaction provides the best agreement with experimental B(E2) transition strengths for the ground-state bands of these nuclei?
• RQ3 Does the FPD6 interaction, which best reproduces level spectra, also yield the most accurate transition probabilities, or is another interaction superior in this regard?
• RQ4 How do different effective charge assumptions (e.g., eπ=0.7e, eν=0.5e) affect the calculated E2 transition strengths compared to experimental data?
• RQ5 To what extent do the theoretical predictions for 46Cr and 46V, especially for 46V, align with available experimental B(E2) values, and how do they compare to prior theoretical models?

Key findings

• FPD6 interaction provides the best agreement with experimental excitation energies for 46Ti, 46Cr, and 46V up to Jπ = 12+.
• Despite its success in energy spectra, FPD6 yields less accurate B(E2) transition strengths compared to GXPF1, particularly for transitions like B(E2; 2⁺₁ → 0⁺₁) and B(E2; 4⁺₁ → 2⁺₁).
• GXPF1 interaction produces transition strengths that are in excellent agreement with experimental B(E2) values for 46Ti, outperforming previous theoretical models such as Th.1 (PPNC), Th.2 (projected HF), Th.3 (MONSTER), Th.4 (f7/2)⁶, and Th.5 (rotational model).
• For 46V, theoretical B(E2) values calculated with GXPF1 show excellent agreement with experimental data for the 2⁺₁ → 0⁺₁ and 4⁺₁ → 2⁺₁ transitions, surpassing earlier theoretical results from Th.2 and Th.3.
• KB3G interaction also provides good agreement with experimental B(E2) values, though slightly less accurate than GXPF1, particularly in the 46Ti case.
• The study concludes that GXPF1 is more consistent with experimental transition strengths than FPD6 in the lower fp-shell region, despite FPD6's superior performance in energy level description.