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Register a new userComputation of spectroscopic factors with the coupled-cluster method
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We present a calculation of spectroscopic factors within coupled-cluster theory. Our derivation of algebraic equations for the one-body overlap functions are based on coupled-cluster equation-of-motion solutions for the ground and excited states of the doubly magic nucleus with mass number $A$ and the odd-mass neighbor with mass $A-1$. As a proof-of-principle calculation, we consider $^{16}$O and the odd neighbors $^{15}$O and $^{15}$N, and compute the spectroscopic factor for nucleon removal from $^{16}$O. We employ a renormalized low-momentum interaction of the $V_{mathrm{low-}k}$ type derived from a chiral interaction at next-to-next-to-next-to-leading order. We study the sensitivity of our results by variation of the momentum cutoff, and then discuss the treatment of the center of mass.
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The precise determination of astrophysical S-factors is essential for a detailed understanding of the nucleosynthesis in its various facets. It is discussed how the Lorentz integral transform (LIT) method can be applied for such a determination. The astrophysical S-factor for the proton-deuteron radiative capture is considered as test case. The importance of a specific many-body basis used for the LIT equation solution is pointed out. The excellent results of the test are discussed.
The spectroscopic factor has long played a central role in nuclear reaction theory. However, it is not an observable. Consequently it is of minimal use as a meeting point between theory and experiment. In this paper the nature of the problem is explored. At the many-body level, unitary transformations are constructed that vary the spectroscopic factors over the full range of allowed values. At the phenomenological level, field redefinitions play a similar role and the spectroscopic factor extracted from experiment depend more on the assumed energy dependence of the potentials than on the measured cross-sections. The consistency conditions, gauge invariance and Wegmanns theorem play a large role in these considerations.
We present an approach to derive effective shell-model interactions from microscopic nuclear forces. The similarity-transformed coupled-cluster Hamiltonian decouples the single-reference state of a closed-shell nucleus and provides us with a core for the shell model. We use a second similarity transformation to decouple a shell-model space from the excluded space. We show that the three-body terms induced by both similarity transformations are crucial for an accurate computation of ground and excited states. As a proof of principle we use a nucleon-nucleon interaction from chiral effective field theory, employ a $^4$He core, and compute low-lying states of $^{6-8}$He and $^{6-8}$Li in $p$-shell model spaces. Our results agree with benchmarks from full configuration interaction.
The reformulated coupled-cluster method (CCM), in which average many-body potentials are introduced, provides a useful framework to organize numerous terms appearing in CCM equations, which enables us to clarify the structure of the CCM theory and physical importance of various terms more easily. We explicitly apply this framework to $^4$He, retaining one-body and two-body correlations as the first illustrating attempt. Numerical results with using two modern nucleon-nucleon interactions (AV18 and CD-Bonn) and their low-momentum interactions are presented. The characters of short-range and many-body correlations are discussed. Although not considered explicitly, the expression of the ground-state energy in the presence of a three-nucleon force is given.
It is extremely important to devise a reliable method to extract spectroscopic factors from transfer cross sections. We analyse the standard DWBA procedure and combine it with the asymptotic normalisation coefficient, extracted from an independent data set. We find that the single particle parameters used in the past generate inconsistent asymptotic normalization coefficients. In order to obtain a consistent spectroscopic factor, non-standard parameters for the single particle overlap functions can be used but, as a consequence, often reduced spectroscopic strengths emerge. Different choices of optical potentials and higher order effects in the reaction model are also studied. Our test cases consist of: $^{14}$C(d,p)$^{15}$C(g.s.) at $E_d^{lab}=14$ MeV, $^{16}$O(d,p)$^{17}$O(g.s.) at $E_d^{lab}=15$ MeV and $^{40}$Ca(d,p)$^{41}$Ca(g.s.) at $E_d^{lab}=11$ MeV. We underline the importance of performing experiments specifically designed to extract ANCs for these systems.
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