Narrow Results

The α+⁶He low-energy reactions and the structural changes of ¹⁰Be in the microscopic α+α+N+N model are studied by the generalized two-center cluster model with the Kohn-Hulthén-Kato variation method. It is found that, in the inelastic scattering to the channel, characteristic enhancements are expected as the results of the parity-dependent non-adiabatic dynamics. In the positive parity state, the enhancement originates from the excited eigenstate generated by the resonance pole of the final channel, while that in the negative parity state is induced by the Landau-Zener level-crossing. The reaction mechanism in breakup of ¹⁰Be into the ⁵He+⁵He and α+⁶He continuums is also studied. The strong enhancement in the breakup of is discussed in connection with the non-adiabatic dynamics.

The ${}^{26}\mathrm{\text{Mg}}{(n,\gamma )}^{27}\mathrm{\text{Mg}}$ reaction plays a crucial role in the process of nucleosynthesis in stars. It occurs primarily in massive stars during their late evolutionary stages or during explosive events like supernovae. This paper focuses on investigating discrepancies in the ANC values of the ${}^{26}\mathrm{\text{Mg}}{(n,\gamma )}^{27}\mathrm{\text{Mg}}$ reaction by analyzing experimental angular distributions of ${}^{26}\mathrm{\text{Mg}}{(d,p)}^{27}\mathrm{\text{Mg}}$ using the DWBA, ADWA and CDCC methods for both ground and first excited states. We then use a mirror nucleus procedure to extract information on the ANCs of the ground state ${}^{26}\mathrm{\text{Si}}{(p,\gamma )}^{27}\mathrm{\text{P}}$ reaction. The Hauser–Feshbach formalism of the statistical Compound Nucleus (CN) model was applied in this study to perform a compound-nucleus analysis of the ${}^{26}\mathrm{\text{Mg}}{(d,p)}^{27}\mathrm{\text{Mg}}$ reaction. The ${}^{26}\mathrm{\text{Mg}}{(d,p)}^{27}\mathrm{\text{Mg}}$ reaction has almost fulfilled the condition of peripherality, which is necessary for understanding the magnitude of the direct reaction contribution. ANCs for the ${}^{27}\mathrm{\text{Mg}}\to {}^{26}\mathrm{\text{Mg}}+n$ virtual decay system were obtained. Moreover, according to charge symmetry of mirror nuclei, the square of proton ANC for a ${}^{27}\mathrm{\text{P}}\to {}^{26}\mathrm{\text{Si}}+p$ is determined and comparison between the values of the presented ANCs.

We have measured the angular distributions for ¹⁶O elastically scattered on ¹²C nuclei at energy 28 MeV and also for ¹²C ion beam elastically scattered on ¹¹B target nuclei at energy 18 MeV. These measurements were performed in the cyclotron DC-60 INP NNC RK. Calculations were performed using both empirical Woods–Saxon and double folding optical model potentials. Both elastic scattering and transfer reaction were taken into consideration. We have extracted the spectroscopic factors for the configurations ¹⁶O → ¹²C + α and ¹²C → ¹¹B + p and compared them with other calculated or extracted values at different energies from literature. The extracted spectroscopic factor for the configuration ¹²C → ¹¹B + p from the current work is in the range 2.7–3.1, which is very close to Cohen–Kurath prediction. While for the configuration ¹⁶O → ¹²C + α, spectroscopic factors show fluctuation with energy which could be due to the well-known resonant-like behavior observed in ¹⁶O + ¹²C excitation function.

The angular distribution measurements for ¹⁶O ion beam elastically scattered from ¹¹B target of thickness 32.9μg/cm² at energy 22.4 MeV had been performed in the cyclotron DC-60 INP NNC RK. The previous measurements for ¹⁶O+¹¹B nuclear system at energies 27, 30, 32.5 and 35 MeV showed an increase in the differential cross-section at backward angles due to the contribution of cluster transfer. Such transfer process could not be described in terms of optical model (OM); it could be described within the framework of distorted wave Born approximation method implemented in FRESCO code. Both one (⁵Li) and two-step transfer (proton transfer followed by Alpha transfer) were taken into considerations. We have extracted the spectroscopic amplitude (SA) for the configuration ¹⁶O→¹¹B+⁵Li.

The reaction ${}^{27}$Al($d$,³He) at 25 MeV beam energy has been utilized to study the states in even–even nucleus ${}^{26}$Mg. The spectroscopic factors have been extracted for the states of ${}^{26}$Mg up to 7.50MeV excitation energy using local, zero-range distorted wave Born approximation. The extracted spectroscopic factors have been compared with the previously reported values. The present results were also compared with the predictions from a theoretical shell model and rotational model.

Cross sections of reaction products were measured in ${}^{28}$Si${+}^{93}$Nb reaction using recoil catcher technique involving by off-line gamma-ray spectrometry at beam energies of 105 and 155MeV. At $E_{\mathrm{\text{lab}}}=155$MeV, the contribution from different incomplete mass transfer processes is investigated. Results of the present studies show the contribution from deep inelastic collision (DIC), massive transfer or incomplete fusion (ICF) and quasi-elastic transfer (QET). The contribution from massive transfer reactions was confirmed from the fractional yield of the reaction products in the forward catcher foil. The present results are different from those from the reactions with comparatively higher entrance channel mass asymmetry with lighter projectiles, for which dominant transfer processes are ICF and QET which involve mass transfer predominantly from projectile to target. The $N/Z$ values of the products close to the target mass were observed to be in a wide range, starting from $N/Z$ of the target (${}^{93}$Nb) and extending slightly below the $N/Z$ of the composite system, consistent with the contribution from DIC and QET reactions. At $E_{\mathrm{\text{lab}}}=105$MeV, a small contribution from QET was observed in addition to complete fusion.

These lectures, held at a school at the Galileo Galilei Institute for Theoretical Physics, give a survey of the formalism, the methods and achievements of nuclear direct reaction theory. After recapitulating the principles of quantum scattering theory, projection techniques are used to reduce the complexities of nuclear reactions to the manageable level of a set of a few selected coupled channels interacting via effective operators. Direct reactions are introduced as fast reactions proceeding preferentially through the excitation of doorway components of the nuclear many-body configurations, corresponding to a separation of scales in energy and momentum transfer. The concept of the optical model is introduced and applied to elastic scattering on nuclei. The coupled channel T-matrix formalism is discussed for pion-induced reactions on the nucleon. Applications of direct reaction to theory are illustrated for transfer reactions, inelastic scattering, and single and double charge exchange reactions with light and heavy ions.

Inspired by the prevalent $n+p$ cluster structure of deuterons, which appears at an excitation energy of 2.225MeV, the recently measured angular distributions (ADs) for ${}^{15}$N($d$,$d{)}^{15}$N and ${}^{15}$N($d$,$p{)}^{16}$N systems at an energy of 15MeV X. Y. Li et al., [Phys. Rev. C 106, (2022) 025807] are microscopically analyzed using the continuum discretized coupled channel (CDCC) method. The extracted $U_{\text{eff}}$ potential, considered as the coherent sum of cluster folding and dynamical polarization potentials, both derived from the CDCC computations, was then employed to investigate the ${}^{15}$N($d$,$p{)}^{16}$N neutron transfer reaction leading to the (2⁻, 0.0MeV), (0⁻, 0.12MeV), (3⁻, 0.298MeV), and (1⁻, 0.397MeV) ${}^{16}$N states. Since extracting reliable information on spectroscopic factors (SFs) is highly dependent on the interaction potential, the extracted $U_{\text{eff}}$ was employed to get such information. The investigation gives evidence for the applicability of the $U_{\text{eff}}$ in describing the elastic scattering and the neutron transfer ADs data. The extracted SFs for the ${}^{16}$N states under consideration are consistent with those that have been reported before.

Angular distributions of protons, deuterons, tritons, and alpha particles emitted in the reaction ²H+⁹Be at E_lab=19.5, 25, and 35 MeV were measured to study the structure of ⁹Be, especially to shed light on the internal clusters and possible cluster transfer of ⁵He. The experiments were performed at sufficiently high energies to ensure suppression of compound nucleus contribution. Thus, the direct reaction mechanism should be mainly responsible for the measured five-nucleon transfer cross section. The analysis suggests a significant contribution of simultaneous five-nucleon transfer in the reaction channel ⁹Be (d,⁴He) ⁷Li.

Radioactive ion beams (RIBs) offer a way to obtain moderately excited nuclei with atomic numbers Z≥100 produced in the multi-nucleon transfer reactions. The choice of suitable RIBs available from the ACCULINNA-2 fragment separator, coupled with the U-400 cyclotron, and possible results of relevant experiments are discussed.

The GODDESS coupling of charged-particle and photon spectrometers has been commissioned using a beam of ¹³⁴Xe at 10 MeV/A. This measurement demonstrates the capability of the device for measuring inelastic scattering and (d,pγ) reactions in inverse kinematics under radioactive beam conditions, and provides the first data on the single-particle structure of states in ¹³⁵Xe, including previously unobserved states based on the orbitals above the N = 82 shell closure.

Over the last two decades transfer reactions have seen a resurgence following developments in methods to use them with exotic beams. An important step in this evolution was the ability to perform the (d,p) reaction on fission fragment beams using the inverse kinematics technique, built on the experience with light beams. There has been renewed interest in using (⁹Be, ⁸Be) and (¹³C, ¹²C) reactions to selectively populate single-particle like states that can be studied via their subsequent γ decay. These reactions have been successfully utilized in the ¹³²Sn region. Additionally, our collaboration has recently performed experiments with GODDESS, a combination of the full ORRUBA detector and Gammasphere arrays. Another new direction is measuring neutrons from (d,n) reactions, performed in inverse kinematics, with the VANDLE array of plastic scintillators. Presented below is an overview of these new techniques and some of the early data from recent experiments.

Single-particle transfer reactions are typically measured at energies where only a peripheral reaction can occur, without probing the interior of the nuclear wave function. At low energies (≈5 MeV/u), spectroscopic factors cannot be reliably extracted without a detailed description of the bound-state potential. Mukhamedzhanov and Nunes have proposed a method to constrain the shape of the bound state potential by combining transfer reaction measurements at two different energies. The external contribution of the wave function is extracted using a peripheral reaction, and is combined with a higher energy measurement which probes the nuclear interior more deeply. These two measurements should constrain the single-particle asymptotic normalization coefficient, ANC, and enable spectroscopic factors to be deduced with uncertainties dominated by the cross-section measurements rather than the bound-state potential. Published measurements of ⁸⁶Kr(d,p) at 5.5 MeV/u were used to determine the external contribution of this reaction. At less-peripheral energies, ⁸⁶Kr(d,p) at 35 MeV/u has been measured in inverse kinematics at the NSCL using the OR- RUBA and SIDAR arrays of silicon strip detectors. Preliminary analysis shows that the single-particle ANC can be constrained. The details of the analysis and prospects for measurements with neutron-rich beams will be presented.

The dynamics of transfer reactions in collisions between two very heavy nuclei ²³⁸U+²³⁸U is studied within the dinuclear system (DNS) model. Collisions between two actinide nuclei form a super-heavy composite system during a very short time, in which a large number of charge and mass transfers may take place. Such reactions have been investigated experimentally as an alternative way for the production of heavy and superheavy nuclei. The role of collision orientation in the production cross sections of heavy nuclides is analyzed systematically. Calculations show that the cross sections decrease drastically with increasing the charged numbers of heavy fragments. The transfer mechanism is favorable to synthesize heavy neutron-rich isotopes, such as nuclei around the subclosure at N=162 from No (Z=102) to Db (Z=105).

The recently discovered possibility of the ‘partial’ conservation of seniority is discussed which arises when most states are of mixed seniority but some remain pure. This phenomenon is explained with use of energy matrices constructed in a seniority basis. The implications of partial conservation of seniority for one-particle transfer reactions are pointed out.

With the development of new radioactive ion beam (RIB) facilities such as FRIB, which will push measurements further away from stability, the need for improved RIB targets is more crucial than ever. Important scattering, transfer and capture reaction measurements of rare, exotic, and unstable nuclei on hydrogen and helium require targets that are dense, highly localized, and pure. To this end, the JENSA Collaboration led by the Colorado ol of Mines (CSM) is designing, building and testing a supersonic gas jet target for use at existing and future RIB facilities. The gas jet target allows for a high density and purity of target nuclei (such as ³He) within a highly confined region, without the use of windows or backing materials, and will also enable the use of state-of-the-art detection systems. The motivation, specifications and status of the CSM gas jet target system is discussed.

The (d,p) reaction was measured with radioactive ion beams of ¹²⁶Sn and ¹²⁸Sn (~5 MeV/u) in inverse kinematics at the Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory, utilizing the SuperORRUBA silicon detector array. Angular distributions of reaction protons were measured for several states in ¹²⁷Sn and ¹²⁹Sn in order to determine angular momentum transfers and deduce spectroscopic factors. Combined with previous experiments on ¹³⁰Sn and ¹³²Sn, these results provide a complete set of (d,p) reaction data on even tin isotopes between stable ¹²⁴Sn and doubly magic ¹³²Sn.

A study of inelastic scattering and single-particle transfer reactions was performed by alpha and ³He beams on a ⁹Be target at energy about 50 MeV. Angular distributions of the differential cross sections for the ⁹Be(α,α')⁹Be*, ⁹Be(α,³He)¹⁰Be, ⁹Be(α,t)¹⁰B, ⁹Be(³He,⁶Li)⁶Li and ⁹Be(³He,⁶Be)6He reactions were measured. Experimental angular distributions of the differential cross sections for the ground state and a few low-lying states were analyzed in the framework of the optical model, coupled channels and distorted-wave Born approximation. The information on the cluster structure of the reaction products are obtained. An analysis of the spectroscopic factors was performed.