Explanation for spectroscopic factor quenching in knockout reactions

Spectroscopic factors are fundamental quantities in nuclear physics. They have been extensively used in understanding the single particle properties of nuclear structures and astrophysical network calculations. Neutron spectroscopic factors of 88 ground state and 565 excited states for Z=3-28 stable nuclei from (d,p) and (p,d) transfer reactions are extracted using a systematic approach with minimum assumptions. This extensive set of data suggests that the extracted spectroscopic factors are in good agreement with the predictions of the large-basis shell-model predictions. The (p,d) neutron transfer reaction measurements have been extended to exotic nuclei of proton-rich Ar and neutron-rich Ar. The experimental results show little reduction of the ground state neutron spectroscopic factor of the proton-rich nucleus Ar compared to that of Ar. The results suggest that correlations, which generally reduce such spectroscopic factors, do not depend strongly on the neutron-proton asymmetry of the nucleus in this isotopic region as was reported in knockout reactions. The present results are consistent with results from systematic studies of transfer reactions and the dispersive-optical model analysis, but are inconsistent with the trends observed in knockout reaction measurements.

<p indent="0mm">In recent decades, experimental studies on the exotic structures of neutron-rich halo nuclei have been one of the hottest topics in nuclear physics. The halo nuclei have the characteristics of large matter radii, long-density tails, and weakly-bound nucleons. Direct nuclear reactions induced by the halo nuclei with several tens of MeV/nucleon on protons and deuterons, including elastic scattering, inelastic scattering, and transfer reactions, are one of the commonly used methods to study the exotic structures of halo nuclei. Together with the experimental work of the Nuclear Physics Experimental Group at Peking University, this paper mainly reviews the relative experimental progress, such as ^6,8He, ¹¹Be, ¹⁴B, ¹⁵C and so on. Differential cross sections extracted from the direct nuclear reaction experiments of halo nuclei are different from those of the stable nuclei, which are very useful for investigating their exotic structures. The elastic scattering differential cross section of ¹¹Be+<italic>p</italic> was better described by using the theoretical calculations of the normalized systematical optical potential parameters and the CDCC (continuum discretized coupled-channels) method, implying the importance of coupling effects for the weak-binding nuclei. Deformation length, <italic>B</italic>(<italic>E</italic>1), <italic>B</italic>(<italic>E</italic>2), as well as the diffraction radius, <italic>R</italic>_dif, of the excitation states can be deduced from the inelastic scattering differential cross sections. The spin-parity, spectroscopic factors, as well as effective single-particle energy extracted from transfer reactions, are useful for investigating the single-particle structure and the shell evolution of unstable nuclei. For example, we found that the ground-state of ¹²Be is dominated by the <italic>d</italic>-wave intruder configuration from the transfer reaction of ¹¹Be(<italic>d</italic>, <italic>p</italic>)¹²Be in inverse kinematics, exhibiting a dramatic evolution of the intruding mechanism from ¹¹Be to ¹²Be, with a persistence of the <italic>N</italic>=8 magic number broken. A resonant state at <inline-formula id="INLINE17"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" mathsize="8.0pt"><mml:mrow><mml:msubsup other="0"><mml:mrow other="0"><mml:mn mathsize="8.0pt" other="0">3.21</mml:mn></mml:mrow><mml:mrow other="1"><mml:mo mathsize="5.6pt" other="1">+</mml:mo><mml:mn mathsize="5.6pt" other="1">0.12</mml:mn></mml:mrow><mml:mrow other="1"><mml:mo mathsize="5.6pt" other="1">−</mml:mo><mml:mn mathsize="5.6pt" other="1">0.04</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> MeV, located just above the one-neutron separation threshold, was observed for the first time in ¹²Be from the same experiment, indicating the importance of continuum coupling. The evolution of <italic>s</italic>- and <italic>d</italic>-wave intruder strength in the ground-state of the <italic>N=</italic>8 isotones, the effective single particle energy of <italic>s</italic>- and <italic>d</italic>-shell in the <italic>N</italic>=9 isotones and in the neutron-rich boron isotopes were systematically investigated by using the direct nuclear reactions. Nucleon-nucleon correlation can affect the occupation number of each shell. The spectroscopic factors extracted from the (e, e′<italic>p</italic>), knock out, as well as transfer reactions are commonly quenched in comparison with the prediction values from the independent particle model, which is often quantified by the quenching factor, <italic>R_s</italic>. Now, from the (e, e′<italic>p</italic>) and knock-out reactions, the conclusions on the relationship between <italic>R_s</italic> and the proton-neutron asymmetry Δ<italic>S</italic> seem to be clear, but not clear from the transfer reaction. Some controversial points focus on the transfer reactions related to the halo nuclei, where the corresponding experiments are limited and the relevant theoretical calculations have a great uncertainty. We completed a combined experiment with the ¹⁵C and ¹⁶N radioactive beams at RIBLL1, Lanzhou to further study this topic and wish to have a clear conclusion for the transfer reaction in the future.

Nuclear structure of 7Be, 8B and 7,8Li is studied within the ab initio\nno-core shell model (NCSM). Starting from high-precision nucleon-nucleon (NN)\ninteractions, wave functions of 7Be and 8B bound states are obtained in basis\nspaces up to 10 hbar Omega and used to calculate channel cluster form factors\n(overlap integrals) of the 8B ground state with 7Be+p. Due to the use of the\nharmonic oscillator (HO) basis, the overlap integrals have incorrect asymptotic\nproperties. We fix this problem in two alternative ways. First, by a\nWoods-Saxon (WS) potential solution fit to the interior of the NCSM overlap\nintegrals. Second, by a direct matching with the Whittaker function. The\ncorrected overlap integrals are then used for the 7Be(p,gamma)8B S-factor\ncalculation. We study the convergence of the S-factor with respect to the NCSM\nHO frequency and the model space size. Our S-factor results are in agreement\nwith recent direct measurement data. We also test the spectroscopic factors and\nthe corrected overlap integrals from the NCSM in describing the momentum\ndistributions in knockout reactions with 8B projectiles. A good agreement with\nthe available experimental data is also found, attesting the overall\nconsistency of the calculations.\n

A review of recent applications of the nonlocal dispersive optical model (DOM) is presented that allows a simultaneous description of nuclear structure and nuclear reactions. An assessment of the quality of the resulting potentials for 40Ca and 48Ca is discussed for the description of the (e, e′p) reaction to valence hole states and the possibility of interpreting the data in terms of absolute spectroscopic factors. The relevance of these results in the context of conflicting interpretations between transfer and knockout reactions is pointed out as well as the importance of proton reaction cross sections for isotopes with neutron excess. Application of the nonlocal DOM to 48Ca incorporates the effect of the 8 additional neutrons and allows for an excellent description of elastic scattering data of both protons and neutrons. The corresponding neutron distribution constrained by all available data generates a prediction for the neutron skin that is larger than most mean-field and available ab initio results. Results are presented for the most recent nonlocal DOM analysis of 208Pb.

Nucleon knockout experiments using beryllium or carbon targets reveal a strong dependence of the quenching factors, i.e., the ratio (hbox {R}_{textrm{s}}) of theoretical to the experimental spectroscopic factors (hbox {C}^2{textrm{S}}), on the proton-neutron asymmetry in the nucleus under study. However, this dependence is greatly reduced when a hydrogen target is used. To understand this phenomenon, exclusive ^{1}text {H}(^{17}text {Ne},2hbox {p}~^{16}text {F}) and inclusive ^{12}text {C}(^{17}text {Ne},2hbox {p}~^{16}text {F})hbox {X}, ^{12}text {C}(^{17}text {Ne},^{16}text {F})hbox {X} as well as ^{1}text {H}(^{17}text {Ne},^{16}text {F})hbox {X} (X-denotes undetected reaction products) reactions with ^{16}text {F} in the ground and excited states were analysed. The longitudinal momentum distribution of ^{16}{textrm{F}} and the correlations between the detached protons were studied. In the case of the carbon target, there is a significant deviation from the predictions of the eikonal model. The eikonal approximation was used to extract spectroscopic factor values hbox {C}^2{textrm{S}}. The experimental hbox {C}^2hbox {S} value obtained with C target is markedly lower than that for H target. This is interpreted as rescattering due to simultaneous nucleon knockout from both reaction partners, ^{17}text {Ne} and ^{12}text {C}.

We report for the first time the discrimination of the core fragment knockout and valence nucleon knockout reaction mechanisms at medium energy range, by the use of the recoil proton tagging technique. Intense 8He beams at 82.3 MeV/u were supplied by the RIPS beam line at RIKEN, and impinged on both hydrogen and carbon targets. Recoil protons were detected in coincidence with the forward moving core fragments and neutrons. The core fragment knockout mechanism is identified through the polar angle correlation and checked by various kinematics relations. This mechanism may be used to extract the cluster structure information of unstable nuclei. On the other hand, with the selection of the tagged valence nucleon knockout mechanism, a narrower peak of 7He ground state is obtained. The extracted neutron spectroscopic factor Sn=0.512(18) is relatively smaller than the no-tagged one, and is in good agreement with the prediction of ab initio Greenʼs function Monte Carlo calculations.

Cluster knockout reactions are expected to reveal the amount of clustering (such as that of α, d and even of heavier clusters such as12C, 16O etc.) in the target nucleus. In simple terms, incident medium high-energy nuclear projectile interacts strongly with the cluster (present in the target nucleus) as if it were existing as a free entity. Theoretically, the relatively softer interactions of the two outgoing particles with the residual nucleus lead to optical distortions and are treated in terms of distorted wave (DW) formalism. The long-range projectile–cluster interaction is accounted for, in terms of the finite range (FR) direct reaction formalism, as against the more commonly adopted zero-range (ZR) distorted wave impulse approximation (DWIA) formalism. Comparison of the DWIA calculations with the observed data provide information about the momentum distribution and the clustering spectroscopic factor of the target nucleus. Interesting results and some recent advancements in the area of (α, 2 α) reactions and heavy cluster knockout reactions are discussed. Importance of the finite-range vertex and the final-state interactions are brought out.