Content uploaded by F. Hammache
Author content
All content in this area was uploaded by F. Hammache on Feb 13, 2014
Content may be subject to copyright.
A preview of the PDF is not available
Experimental Study of the Two-Body Spin-Orbit Force in Nuclei
Abstract and Figures
Energies and spectroscopic factors of the first 7/2-, 3/2-, 1/2-, and 5/2- states in the Si2135 nucleus were determined by means of the (d, p) transfer reaction in inverse kinematics at GANIL using the MUST2 and EXOGAM detectors. By comparing the spectroscopic information on the Si35 and S37 isotones, a reduction of the p3/2-p1/2 spin-orbit splitting by about 25% is proposed, while the f7/2-f5/2 spin-orbit splitting seems to remain constant. These features, derived after having unfolded nuclear correlations using shell model calculations, have been attributed to the properties of the two-body spin-orbit interaction, the amplitude of which is derived for the first time in an atomic nucleus. The present results, remarkably well reproduced by using several realistic nucleon-nucleon forces, provide a unique touchstone for the modeling of the spin-orbit interaction in atomic nuclei.
Figures - uploaded by F. Hammache
Author content
All figure content in this area was uploaded by F. Hammache
Content may be subject to copyright.
... The original TIARA setup was extended subsequently, with the addition of MUST2 telescopes [14] in the forward direction and this is shown in Fig. 1. This setup was able to discover the unbound intruder νf 7/2 state in 27 Ne, also using the (d, p) reaction. Further, however, the bound νp 3/2 intruder state at 765 keV was positively identified using a combination of both the γray information and the proton angular distribution [15]. ...
... In the case of the 34 Si(d, p) study, an ionisation chamber was placed upstream with respect to the plastic, so allowing for the selection of the Si residues. The results obtained for the 34 Si(d, p) reaction are reported in Ref. [27]. Energies and spectroscopic factors of states populated in 35 Si have evidenced a reduction by about 25% of the νp 3/2 -νp 1/2 spin-orbit splitting, while the νf 7/2νf 5/2 spin-orbit splitting seemed to remain constant. ...
... A transfer experiment has however been performed using the γ -ray tracking array GRETINA [46] which in the USA is present implementation of the complete 4π GRETA array which is under construction. The experiment itself [47] was again astrophysically motivated and ingeniously used the (d, p) neutron transfer reaction on the 0 + ground state of 26 Si in order to study proton capture onto the isomeric excited 0 + state of 26 Al, the isobaric analogue of the 26 Si ground state: a mirror reaction on a mirror nucleus to reach the identical final state in 27 Si. The γ -emitting nuclei were moving at 0.25c and the γ rays of interest extended up to energies above 6 MeV. ...
In recent decades, $$\gamma $$ γ -ray spectroscopy has undergone a major technological leap forward, namely the technique of $$\gamma $$ γ -ray tracking, and has attained a sensitivity that is two orders of magnitude larger than that provided by the former generation of Compton-shielded arrays. Indeed the gain is comparable with the achievements since the dawn of $$\gamma $$ γ -ray spectroscopy. Such sensitivity can be further heightened by coupling $$\gamma $$ γ -ray spectrometers to other detectors that record complementary reaction products such as light-charged particles for transfer reactions and scattered ions for Coulomb excitation measurements. Nucleon transfer reactions offer an excellent mean to probe the energies of shell model single-particle orbitals and to study migration in energy of these orbitals as we venture away from stability. Such measurements can also estimate the cross sections of processes relevant to stellar evolution and nucleosynthesis. The measurement of $$\gamma $$ γ rays in coincidence with particles provides also information on the decay channel for unbound systems, which constitutes a useful input for astrophysics and nuclear structure near the drip-lines. Coulomb-excitation studies make it possible to infer collective structure in nuclei and to extract deformation properties of, in particular, open-shell systems. Here, selected examples will be presented, highlighting the power of these types of experiments when $$\gamma $$ γ -ray observation is included. The development of the experimental methods is reviewed, showing the results achieved before the advent of $$\gamma $$ γ -ray tracking. Examples of more recent experiments that have successfully exploited $$\gamma $$ γ -ray tracking with AGATA are then presented as showcases for the outstanding performance of the composite detection systems. The outlook for experiments using newly developed devices such as GRIT and other detectors such as SPIDER is described.
... For a unified description of the shell evolution, in [13], it was proposed that the central and tensor forces are the major sources of shell evolution, whereas the two-body spin-orbit force plays a unique role in the monopole matrix elements between specific orbitals [14]. The same conclusion was drawn from the spin-tensor decomposition of an effective interaction fitted to the experimental data [15]. ...
... Next, the evolution of the N = 32 shell gap is discussed. The 34 Si(d, p) reaction experiment in inverse kinematics found two prominent l = 1 peaks at 0.910 and 2.044 MeV, the former and the latter of which should be the 3/2 − and 1/2 − levels, respectively [14]. The interval of these two levels, 1.134 MeV, is much smaller than the corresponding value of 37 S, 1.911 MeV. ...
In this paper, the validity of the shell-evolution picture is investigated on the basis of shell-model calculations for the atomic mass number 25≲A≲55 neutron-rich nuclei. For this purpose, the so-called SDPF-MU interaction is used. Its central, two-body spin–orbit, and tensor forces are taken from a simple Gaussian force, the M3Y (Michigan 3-range Yukawa) interaction, and a π+ρ meson exchange force, respectively. Carrying out almost a complete survey of the predicted effective single-particle energies, it is confirmed here that the present scheme is quite effective for describing shell evolution in exotic nuclei.
... With an increase in the neutron number, the energy gap at Z = 16 diminishes, establishing the groundwork for the disappearance of the shell structure at N = 28 and underscoring the importance of 3NF in describing shell evolution. Moreover, through the application of the spin-tensor decomposition method [26,77,79], it becomes possible to isolate different components of the effective N N interaction, facilitating a qualitative analysis of contributions of specific components to the evolution of ESPE. Fig. 6(b) compares the calculated ESPEs with and without considering tensor forces based on the effective Hamiltonian derived from N N + 3N (lnl) interaction. ...
Neutron-rich P, Cl, and K isotopes, particularly those with neutron numbers around $N=28$, have attracted extensive experimental and theoretical interest. We utilize the \textit{ab initio} valence-space in-medium similarity renormalization group approach, based on chiral nucleon-nucleon and three-nucleon forces, to investigate the exotic properties of these isotopes. Systematic calculations of the low-lying spectra are performed. A key finding is the level inversion between $3/2_1^+$ and $1/2_1^+$ states in odd-$A$ isotopes, attributed to the inversion of $\pi 0d_{3/2}$ and $\pi 1s_{1/2}$ single-particle states.\textit{Ab initio} calculations, which incorporate the three-nucleon forces, correlate closely with existing experimental data. Further calculations of effective proton single-particle energies provide deeper insights into the shell evolution for $Z=14$ and $16$ sub-shells. Our results indicate that the three-body force plays important roles in the shell evolution for $Z=14$ and $16$ sub-shells with neutron numbers ranging from 20 to 28. Additionally, systematic \textit{ab initio} calculations are conducted for the low-lying spectra of odd-odd nuclei. The results align with experimental data and provide new insights for future research into these isotopes, up to and beyond the drip line.
... As presented in Table III, its high E x (2 + 1 ) [76] and E x (0 + 2 ) [73], combining the small B(E 2; 0 + 1 → 2 + 1 ) [77], are direct indications of shell closure. Additionally, experimental data on neutron and proton occupation in 34 Si [78][79][80] and neutron single-particle structure in 35 Si [81] validated this interpretation. In some of the shellmodel calculations, however, the 0p0h component is reduced to 60% (SDPF-M) and even 20% (EEdf1), showing less doubly-magic features. ...
Background: The nucleus Mg32 (N=20 and Z=12) plays a central role in the so-called “island of inversion,” where in the ground states sd-shell neutrons are promoted to the fp-shell orbitals across the shell gap, resulting in the disappearance of the canonical neutron magic number N=20.
... As presented in Table III, its high E x (2 + 1 ) [76] and E x (0 + 2 ) [73], combining the small B(E2; 0 + 1 → 2 + 1 ) [77], are direct indications of shell closure. Additionally, experimental data on neutron and proton occupation in 34 Si [78][79][80] and neutron single-particle structure in 35 Si [81] validated this interpretation. In some of the shell-model calculations, however, the 0p0h component is reduced to 60 % (SDPF-M) and even 20 % (EEdf1), showing less doubly-magic features. ...
Background: The nucleus $^{32}$Mg ($N=20$ and $Z=12$) plays a central role in the so-called "island of inversion" where in the ground states $sd$-shell neutrons are promoted to the $fp$-shell orbitals across the shell gap, resulting in the disappearance of the canonical neutron magic number $N=20$. Purpose: The primary goals of this work are to extend the level scheme of $^{32}$Mg, provide spin-parity assignments to excited states, and discuss the microscopic structure of each state through comparisons with theoretical calculations. Method: In-beam $\gamma$-ray spectroscopy of $^{32}$Mg was performed using two direct-reaction probes, one-neutron (two-proton) knockout reactions on $^{33}$Mg ($^{34}$Si). Final-state exclusive cross sections and parallel momentum distributions were extracted from the experimental data and compared with eikonal-based reaction model calculations combined with shell-model overlap functions. Results: Owing to the remarkable selectivity of the one-neutron and two-proton knockout reactions, a significantly updated level scheme for $^{32}$Mg, which exhibits negative-parity intruder and positive-parity normal states, was constructed. The experimental results were confronted with four different nuclear structure models. Conclusions: In some of these models, different aspects of $^{32}$Mg and the transition into the island of inversion are well described. However, unexplained discrepancies remain, and even with the help of these state-of-the-art theoretical approaches, the structure of this key nucleus is not yet fully captured.
... The symbols are the centroids for 37 S [42],39 Ar[50], and 41 Ca[50,51]. The horizontal bars are the energy differences between relevant highest peaks[50,52]. Shell evolution predictions are shown by blue closed symbols and the solid line connecting them. ...
Some emerging concepts of nuclear structure are overviewed. (i) Background: the many-body quantum structure of atomic nucleus, a complex system comprising protons and neutrons (called nucleons collectively), has been studied largely based on the idea of the quantum liquid (à la Landau), where nucleons are quasiparticles moving in a (mean) potential well, with weak “residual” interactions between nucleons. The potential is rigid in general, although it can be anisotropic. While this view was a good starting point, it is time to look into kaleidoscopic aspects of the nuclear structure brought in by underlying dynamics and nuclear forces. (ii) Methods: exotic features as well as classical issues are investigated from fresh viewpoints based on the shell model and nucleon–nucleon interactions. The 70-year progress of the shell–model approach, including effective nucleon–nucleon interactions, enables us to do this. (iii) Results: we go beyond the picture of the solid potential well by activating the monopole interactions of the nuclear forces. This produces notable consequences in key features such as the shell/magic structure, the shape deformation, the dripline, etc. These consequences are understood with emerging concepts such as shell evolution (including type-II), T-plot, self-organization (for collective bands), triaxial-shape dominance, new dripline mechanism, etc. The resulting predictions and analyses agree with experiment. (iv) Conclusion: atomic nuclei are surprisingly richer objects than initially thought.
Neutron-rich P, Cl, and K isotopes, particularly those with neutron numbers around $N=28$, have attracted extensive experimental and theoretical interest. We utilize the \textit{ab initio} valence-space in-medium similarity renormalization group approach, based on chiral nucleon-nucleon and three-nucleon forces, to investigate the exotic properties of these isotopes. Systematic calculations of the low-lying spectra are performed. A key finding is the level inversion between $3/2_1^+$ and $1/2_1^+$ states in odd-$A$ isotopes, attributed to the inversion of $\pi 0d_{3/2}$ and $\pi 1s_{1/2}$ single-particle states. \textit{Ab initio} calculations, which incorporate the three-nucleon forces, correlate closely with existing experimental data. Further calculations of effective proton single-particle energies provide deeper insights into the shell evolution for $Z=14$ and $16$ sub-shells. Our results indicate that the three-body force plays important roles in the shell evolution for $Z=14$ and $16$ sub-shells with neutron numbers ranging from 20 to 28. Additionally, systematic \textit{ab initio} calculations are conducted for the low-lying spectra of odd-odd nuclei. The results align with experimental data and provide new insights for future research into these isotopes, up to and beyond the drip line.
Regarding the stage progress on the relativistic Hartree-Fock (RHF) model achieved recently, we review the extensive developments of the model itself, including the descriptions of axially deformed unstable nuclei and nuclear spin-isospin excitations, which shows that a complete RHF framework is now available for such as exploring the tensor force effects in both ground state and excited states of unstable nuclei. Meanwhile, the recent RHF descriptions of the pseudo-spin symmetry restoration and the new magicity are also reviewed. It shows that the Fock terms, particularly the $\rho$-tensor coupling and naturally introduced tensor force components, bring about significant improvements in maintaining the delicate in-medium balance of nuclear attractions and repulsions, and uniformly interpreting the emergence of new magicity in $^{52,54}$Ca. The revealed microscopic mechanisms not only deepen our understanding on the properties of nuclear structure, but also help to guide the further development of the effective nuclear force.
The systematic search of axial ground state and the emergence of new gaps in neutron-rich [Formula: see text]Ar isotopes are the challenging of current calculations of relativistic and nonrelativistic mean field models. For this purpose, we have employed the model based on Relativistic Hartree–Bogoliubov (RHB) with the density-dependent effective interaction of point coupling DD-PCX type. However, the nonrelativistic mean field calculations based on Hartree-Fock model were carried out with Skyrme SV-min parametrization. All the present calculations were performed within axial symmetries. The results provide that most of isotopes show an oblate-deformed ground state. In particular, [Formula: see text]Ar and [Formula: see text]Ar display a spherical shape in their ground states with SV-Min calculations. There is a notable signature of the sub-shell closure at neutron number [Formula: see text], whereas [Formula: see text] is expected to be nearly quenched in the spherical ground. Furthermore, coexistence features are predicted in the neutron-rich [Formula: see text]Ar isotope. We have also studied the neutron axial densities and its central depletion in the well-deformed grounds for the first time. In addition to these, the proton single-particle evolution and bubble-like structure at [Formula: see text]Ar are very well reproduced with DD-PCX calculations.
The 02+ state in 34Si has been populated at the GANIL-LISE3 facility through the β decay of a newly discovered 1+ isomer in 34Al of 26(1) ms half-life. The simultaneous detection of e+e- pairs allowed the determination of the excitation energy E(02+)=2719(3) keV and the half-life T1/2=19.4(7) ns, from which an electric monopole strength of ρ2(E0)=13.0(0.9)×10-3 was deduced. The 21+ state is observed to decay both to the 01+ ground state and to the newly observed 02+ state [via a 607(2) keV transition] with a ratio R(21+→01+/21+→02+)=1380(717). Gathering all information, a weak mixing with the 01+ and a large deformation parameter of β=0.29(4) are found for the 02+ state, in good agreement with shell model calculations using a new sdpf-u-mix interaction allowing np-nh excitations across the N=20 shell gap.
Cross sections for proton knockout observed in (e,e^{'}p) reactions are apparently quenched by a factor of ∼0.5, an effect attributed to short-range correlations between nucleons. Here we demonstrate that such quenching is not restricted to proton knockout, but a more general phenomenon associated with any nucleon transfer. Measurements of absolute cross sections on a number of targets between ^{16}O and ^{208}Pb were analyzed in a consistent way, with the cross sections reduced to spectroscopic factors through the distorted-wave Born approximation with global optical potentials. Across the 124 cases analyzed here, induced by various proton- and neutron-transfer reactions and with angular momentum transfer ℓ=0-7, the results are consistent with a quenching factor of 0.55. This is an apparently uniform quenching of single-particle motion in the nuclear medium. The effect is seen not only in (d,p) reactions but also in reactions with A=3 and 4 projectiles, when realistic wave functions are used for the projectiles.
The spectra of the nuclei O18, F18, Pb206, Pb210 are calculated using realistic forces and a Woods-Saxon form for the shell-model average field. The substitution of Woods-Saxon for harmonic-oscillator single-particle wave functions leads to appreciable upward shifts in the calculated positions for many low-lying levels in the A=18 nuclei. In particular the T=0, J=1+ and T=1, J=0+ binding energies are decreased by 0.6-1.7 MeV. In the heavier nuclei, one finds significant changes in observed energy levels perhaps only for the ground states. Nevertheless, the introduction of the more realistic single-particle average field in the Pb isotopes and in neighboring nuclei permits one to improve the conceptual basis upon which this field is erected.
The S36(d,p)S37 reaction was studied at Ed=25 MeV with an enriched S36 target (81.1%) and momentum analysis of the protons. Twenty-six groups were identified with levels in S37. Excitation energies were obtained with an uncertainty of ns yielded l and S values for the transfer reaction. Comparison is made to local systematics and the l=1 strength is also compared to recent (n,γ) results. The S34,36(d,He3)P33,35 reactions were also studied. A mass excess for P35 of -24854(5) keV was obtained. (d,He3) proton pickup strength was observed to four states of P35 and seven states of P33. These results are compared to predictions of Wildenthal.
DOI:https://doi.org/10.1103/PhysRev.96.1160
The achromatic spectrometer LISE installed at GANIL is used for the production and identification of either very neutron- or proton-rich nuclei obtained in the fragmentation of intermediate-energy heavy-ion beams at 0°. The characteristics and advantages of the system are described. Deceased on April 11, 1985.
DOI:https://doi.org/10.1103/PhysRev.75.1766.2
A beam detector system, CATS (Chambre A Trajectoires de Saclay), was designed to provide event-by-event particle tracking in experiments with radioactive beams at GANIL. It consists of two low pressure multiwire proportionnal chambers with one plane of anode wires placed between two cathode planes (active area: 70×70 mm2), respectively segmented into 28 vertical or horizontal strips (2.54 mm wide). The anode wires deliver a time signal allowing a time of flight measurement with an accuracy between 440 ps and 1.2 ns, depending on the energy loss of incident particles in the detector. The cathode strips are individually read out and the position of incoming particles is reconstructed using a charge centroid finding algorithm. A spatial resolution of 400 μm (700 μm) was achieved during in beam experiment, with a counting rate of 1.5×105 (106) particles per second.
The neutron-rich isotopes with Z⩽20, in particular those with neutron numbers around N=28, have been the focus of a lot experimental and theoretical scrutiny during the past few years. Shell-model calculations using the effective interaction SDPF-NR were able to predict or to explain most of the properties featured by these nuclei. Prominent among them is the disappearance of the N=28 shell closure for Z⩽16. We have incorporated into SDPF-NR some modifications, either on purely theoretical grounds or guided by new experimental information. The proposed interaction SDPF-U offers enhanced reliability with respect to the earlier version.