Session EL: Mini-Symposium on Nuclear Matter in Neutron Stars II (Symmetry Energy and Hypernuclei)

Constraining the EoS of neutron-rich matter by laboratory measurements

The density and momentum dependencies of the symmetry energy play an important role in the masses, isobaric analog states, low-lying E1 strength functions, neutron skins, giant resonances of neutron rich nuclei, and the isospin dependence of transport and emission during nuclear collisions. It also governs the internal structure of neutron stars, influences their radii and cooling rates as well as the neutrino transport in core-collapse supernova. This talk will discuss some current experimental constraints on the density and momentum dependence of the symmetry energy. It will also discuss future plans to extend these constraints to densities greater than that found in nuclei and similar to those found in the interiors of neutron stars.   

Scaling properties of light-cluster production

We show, using the experimental data from Ca+Ca and Sn+Sn collisions, that ratios of light-particle energy spectra display scaling properties that can be accurately described by effective local chemical potentials. This demonstrates the equivalence of t/3He and n/p spectral ratios and provides an essential test of theoretical predictions of isotopically resolved light-particle spectra. In addition, this approach allows direct comparisons of many theoretical n/p spectral ratios to experiments where charged-particle spectra but not neutron spectra are accurately measured. Such experiments may provide much more quantitative constraints on the density and momentum dependence of the symmetry energy.   

Momentum dependence of symmetry energy

One of the main uncertainties in the Equation of State of neutron-rich nuclear matter concerns the density and momentum dependence of the nuclear symmetry energy. Some constraints on the density dependence of the symmetry energy at sub-saturation densities have been recently obtained. However questions remain, especially concerning the momentum dependence of the symmetry mean-field potential that can make the neutron and proton effective masses different. We probe the momentum dependence of this isovector mean-field potential by comparing the energy spectra of neutrons and protons emitted in $^{112}$Sn+$^{112}$Sn and $^{124}$Sn+$^{124}$Sn collisions at incident energies of E/A=50 and 120 MeV. We achieve an experimental precision that can discriminate between transport model predictions for the n/p double ratio for different momentum dependencies of the symmetry mean-field potential.   

Electric dipole response of nuclei studied by proton inelastic scattering: neutron thickness, symmetry energy, and pygmy dipole resonance

Electric dipole (E1) responses of heavy nuclei have been studied by high-resolution measurement of proton inelastic scattering at forward angles including zero degrees. Here the proton scattering at 300 MeV is used as an electromagnetic probe to extract precisely the distribution of \textit{E1} reduced transition probability $B$(\textit{E1}). The measurement has been done on various stable nuclei such as $^{\mathrm{208}}$Pb, $^{\mathrm{120}}$Sn, $^{\mathrm{90}}$Zr, $^{\mathrm{154}}$Sm, and $^{\mathrm{96}}$Mo. The dipole polarizability and pygmy dipole resonance (PDR) strength has been extracted. Those quantities are considered to have strong correlations to the neutron skin thickness and the first order density dependence of the symmetry energy of the nuclear equation of state. We will present the experimental methods and highlights of the results as well as the preliminary ones of recent analyses.   

Correlation between density-dependence of symmetry energy and electric dipole strength in unstable nuclei

Equation of state (EOS) is again shot into the limelight by discovery of the two-solar-mass neutron star. That heavy neutron star eliminates inadequate EOSs which can not support two-solar-mass neutron stars. Now there are several attempts to constrain the neutron matter EOS. In nuclear physics, it is expected to clarify density-dependence of the nuclear symmetry energy, $L$. We focus our attentions to dipole polarizability of unstable nuclei which has neutron skin. Since the neutron skin is approximately neutron matter, we believe that dynamics of unstable nuclei is affected by the neutron skin and we can extract the properties of neutron matter from it. Although some theoretical calculations using the random-phase approximation demonstrate a strong correlation between $L$ and the dipole polarizability, almost all calculations are performed only for 3 nuclei, 68Ni, 132Sn, and 208Pb with a single interaction. There remains uncertainties on interaction and nuclide dependence. We performed a systematic calculation of the $E1$ modes with several interactions. We show that the correlation between $L$ and the dipole polarizability has somewhat depends on interactions and nuclide and that 54Ca, 140Sn are more suitable for extracting constraint on $L$ from the experiments.   

Strangeness in neutron star matter: a challenging puzzle

The onset of strange baryons in the core of neutron stars and the consequent softening of the equation of state have been questioned for a long time. Controversial theoretical predictions about the predicted maximum mass and the recent astrophysical observations are the grounds of the so called \emph{hyperon puzzle}. We attempt to give our contribution to the discussion by studying the general problem of the hyperon-nucleon interaction by means of Auxiliary Field Diffusion Monte Carlo calculations. We employ a phenomenological approach showing that a three-body hyperon-nucleon force provides the strong repulsive contribution needed to correctly describe the systematics of medium-light $\Lambda$~hypernuclei. The same potential has been used to determine the equation of state and the mass-radius relation of an infinite systems of neutrons and $\Lambda$~particles. We find that the three-body hyperon-nucleon force has a dramatic effect on the equation of state and the predicted maximum mass. Our results suggest that more constraints on the nature of hyperon-neutron forces are needed before drawing any conclusion on the role played by hyperons in neutron stars.   

Neutron Dripline for Magnesium nuclei and hypernuclei

Hypernuclei containing lambda ($\Lambda)$-hyperons are of current interest in nuclear as well as astro-physics. The effect of addition of a $\Lambda $-hyperon on the neutron-dripline of a Magnesium nucleus is investigated in a microscopic framework using the Frankfurt chiral effective model. The chiral flavor-SU(3) yields a good fit to nuclei as well as reproduces 2-solar-mass neutron stars. In this model, we find that the neutron dripline is at $^{42}$Mg. If a $\Lambda $-hyperon is added, it opens up an additional degree of freedom, allowing for a wider energy distribution, and leads to a dripline at $^{51}_{\Lambda}$Mg. The general behavior of additional binding is expected in hyper-nuclei; however the size of the shift is quite striking. When the calculations are repeated with the SPL-40 and NL-3 parameter sets, the dripline nuclei without and with a $\Lambda $-hyperon are found to be $^{52}$Mg and $^{47}_{\Lambda}$Mg (for SPL-40) and $^{46}$Mg and $^{47}_{\Lambda}$Mg (for NL3), respectively. The last experimentally measured nucleus of the Mg isotope chain is $^{40}$Mg which, according to a macroscopic model, is the last bound neutron-rich Mg-isotope. The macroscopic and all three microscopic models well describe the measured $\Lambda $-separation energy of all $\Lambda -$hypernuclei. But, the results near the drip line are found to be very model dependent. Especially, while the SU(3) model suggests that the addition of a $\Lambda $-hyperon leads to an outward shift of the dripline by 8 neutrons, the SPL-40 model indicates an inward shift by rejecting 6 neutrons. Both results are remarkable and calls for experimental verification.   

Photoproduction of medium-mass hypernuclei with $\Lambda$-rotation coupling

Recently hypernuclei beyond p-shell region attract particular interests, because the (e, e'K$+)$ reaction will provide $\Lambda $ single-particle behavior with good energy resolution and also because they offer new opportunity of understanding coupling features between a $\Lambda $ hyperon with nuclear collective motion such as rotation. Based on the preceding study for photo-production of $\Lambda $28Al, $\Lambda $40K, and $\Lambda $52V, here we additionally choose two typical examples, $\Lambda $27Mg and $\Lambda $59Co, in which each nuclear core shows clear ground rotational spectrum, and several energy levels are predicted to have sizable production cross sections in (e, e'K$+)$ experiments to be done at Jefferson Lab. Major calculated results and discussions will be presented.   

Productions of sd-shell hypernuclei $_{\Lambda}^{19}$F and $_{\Lambda}^{20}$Ne in shell-model calculations

Detailed hypernuclear studies have been mainly focused on structures of $s$- and $p$-shell systems. As the next stage of hypernuclear studies, experiments of $sd$-shell hypernuclei will be carried out at J-PARC. The level structures of $sd$-shell nuclei are richer and more complex than those of $p$-shell nuclei. Even the $\Lambda$ single-particle energies are not well known experimentally, and the theoretical study on the interplay with nuclear core excitations have just started in these medium-mass systems. We anticipate innovated $(K^{-}, \pi^{-})$ reaction experiments to be done at J-PARC, as well as $(e, e^{\prime}K^{+})$ reaction experiments at JLab and Mainz. In this work, we focus on $_{\Lambda}^{19}$F and $_{\Lambda}^{20}$Ne hypernuclei and calculate wave functions by using a multi-configuration shell model and the conventional $\Lambda N$ effective interactions derived from the Nijmegen NSC97f potentials. We estimate production cross sections of $(K^{-}, \pi^{-})$, $(\pi^{+}, K^{+})$ and $(e, e^{\prime}K^{+})$ reactions and analyze differences of characteristics between these reactions.   

Search for $^6_\Lambda$H hypernucleus by the ($\pi^-,K^+$) reaction at $p_\pi$=1.2GeV/c

The study of neutron-rich hypernuclei is one of the most important topics in the strangeness nuclear physics. The glue-like role of the $\Lambda$ hyperon is expected to be critical in nuclei beyond the neutron-drip line. The knowledge of the behavior of hyperons in a neutron-excess environment will significantly affect our understanding of neutron stars because the addition of hyperons softens the Equation of State of matter at the core. To study its effects, we selected the $^6_\Lambda$H hypernucleus. An experiment was proposed aiming at a precise spectroscopic investigation of the light neutron-rich hypernucleus $^6_\Lambda$H by the ($\pi^-,K^+$) reaction. The experiment was performed at the K1.8 beam line of the J-PARC Hadron Experimental Facility. Since the cross section of the ($\pi^-,K^+$) reaction is considerably small, high intensity pion beams of 12-14 M/spill were used. Totally $1.4 \times 10^{12}$ were irradiated on a $^6$Li target. In this talk, details of the data analysis will be presented and the physical meaning of the first results will be discussed.   

Observation of a $K^-pp$-like structure in the $d(\pi^+,K^+)$ reaction at 1.69 GeV/$c$

While the existence of kaonic nuclei has been intensively studied both theoretically and experimentally, there is no conclusive result establishing its existence. Here, we have searched for the $K^-pp$, a bound state of a $K^-$ with two protons, in the $d(\pi^+, K^+)$ reaction at 1.69 GeV/$c$ at J-PARC K1.8 beam line with a missing-mass resolution of 2.7 MeV/$c^2$(FWHM). In this reaction, the $K^-pp$ is assumed to be produced as $\Lambda(1405)$ as a doorway such as $\pi^+n \to K^+\Lambda^*$, $\Lambda^*p \to K^-pp$. Since the sticking probability of the $\Lambda^*$ on proton would not be so large, coincidence of high-momentum ($>$ 250 MeV/$c$) proton(s) in large emission angles ($39^\circ<\theta_{lab.}<122^\circ$) was requested to enhance the signal-to-background ratio. We have obtained an inclusive $(\pi^+, K^+)$ spectrum in a wide missing-mass range from $\Lambda$, $\Sigma$ to $\Lambda(1405)$/$\Sigma(1385)$, for the first time. A proton coincidence spectrum shows a large proton-emission probability at around 2.27 GeV/$c^2$ as a broad bump. It might be attributed to the $K^-pp$ production. A study of decay branch suggests non-mesonic decays of $\Lambda N$ and $\Sigma N$ are dominant rather than mesonic decays. We will report the results both on inclusive and coincidence analyses.   

Superdeformed states in hypernuclei with antisymmetrized molecular dynamics

One of the main purposes of hypernuclear physics is to reveal the responses to the addition of a $\Lambda$ particle in (hyper)nuclei. Recently, as an example of such responses, several authors investigated the difference of B$_{\Lambda}$ between the spherical (ground) and largely deformed (superdeformed) states. For example, the relativistic mean-field (RMF) calculations predicted the large B$_{\Lambda}$ in the superdeformed states in several $\Lambda $ hypernuclei such as $^{37}_{\Lambda}$Ar and $^{39}_{\Lambda}$Ar [1]. On the other hand, in $^{41}_{\Lambda}$Ca and $^{46}_{\Lambda}$Sc, it was discussed that B$_{\Lambda}$ in the spherical states is larger than that in the superdeformed states based on the antisymmetrized molecular dynamics (AMD) [2]. In the present study, we have applied the AMD to Ar $\Lambda $ hypernuclei to reveal the difference of B$_{\Lambda}$ between the spherical and superdeformed states. Especially, we will focus on $^{39}_{\Lambda}$Ar as well as $^{37}_{\Lambda}$Ar, because it would be possible to produce $^{39}_{\Lambda}$Ar by the JLab experiments. In this talk, we will show the difference of B$_{\Lambda}$ in Ar hypernuclei and compare it with the previous AMD results and RMF predictions. Furthermore, we will predict the changes of the excitation spectra in $^{39}_{\Lambda}$Ar due to the difference of B$_{\Lambda}$.\\[4pt] [1] B.-N. Lu, \textit{et al.}, Phys. Rev. C\textbf{89}, 044307(2014).\\[0pt] [2] M. Isaka, \textit{et al.}, Phys. Rev. C\textbf{89}, 024310(2014).