Nucleon-nucleon Short-range Correlations Research Articles

Probing heavy-ion collisions with the yield ratios of neutron-proton at intermediate energy

Within an isospin- and momentum-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, we investigate effects of nucleon-nucleon short-range correlations (SRCs) and the nuclear symmetry energy on the yield ratios of neutron-proton (n/p) in four reaction systems K94r+94Kr, Z94r+94Zr, M94o+94Mo and R94u+94Ru. It is found that effects of the symmetry energy and the high momentum tails (HMTs), caused by the SRCs of nucleon-nucleon in the target and projectile, on the kinetic energy distribution of n/p yield ratio are almost same in four reaction systems. While the effect of the HMTs on the double ratio of n/p from neutron-rich and neutron-deficient reaction systems K94r+94Kr and R94u+94Ru is enlarged, and it is about two times than that of the symmetry energy in the high kinetic energies. Meanwhile, we find that the dependence of isospin-fractionation (i.e., the double ratio of n/p of gas-liquid phase) on the isospin asymmetry of reaction system is completely not sensitive to the HMTs but keeping high sensitivity to the symmetry energy. It indicates that the distribution of isospin-fractionation on the isospin asymmetry of reaction system can be taken as an experimental observable to extract information on nuclear symmetry energy.

Effects of nucleon-nucleon short-range correlations on inclusive electron scattering

The nucleon-nucleon short-range correlation (NN-SRC) is one of the key issues of nuclear physics, which typically manifest themselves in high-momentum components of the nuclear momentum distributions. In this paper, the nuclear spectral functions based on the axially deformed relativistic mean-field model are developed to involve the NN-SRC. With the spectral functions, the inclusive electron scattering $(e,{e}^{\ensuremath{'}})$ cross sections are calculated within the plane-wave impulse approximation (PWIA) framework, including the quasielastic (QE) part and $\mathrm{\ensuremath{\Delta}}$ production part. Especially in the $\mathrm{\ensuremath{\Delta}}$ production region, we reconsider the electromagnetic structures of the nucleon resonance $\mathrm{\ensuremath{\Delta}}$(1232) and the scattering mechanisms, and thereby the theoretical calculations are improved effectively and the cross sections are well consistent with the experimental data. The theoretical $(e,{e}^{\ensuremath{'}})$ cross sections are further divided into NN-SRC and mean-field contributions. It is found that, at the kinematics $0.5\phantom{\rule{0.16em}{0ex}}{\mathrm{GeV}}^{2}<{Q}^{2}<1\phantom{\rule{0.16em}{0ex}}{\mathrm{GeV}}^{2}$, the QE peak and $\mathrm{\ensuremath{\Delta}}$ production peak not only reflect the mean-field structure but also are sensitive to the NN-SRC information. Finally, we provide another method to extract the strengths of NN-SRC from experimental cross sections for selected nuclei at the suitable kinematics.

Symmetry energy extracted from the SπRIT pion data in Sn+Sn systems

With the improved particular Isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model (impIBUU) including the nucleon-nucleon short-range correlations, the ratios and yields of $\pi^{-}$ and $\pi^{+}$ in Sn+Sn systems with different asymmetries at 270 MeV/nucleon are studied. It is found that the yields of $\pi^{-}$ and $\pi^{+}$ and their ratios in Sn+Sn systems characterized by different neutron to proton ratios obtained from the very recent S$\pi$RIT pion data, are quite well described by the model, especially when a soft symmetry energy with $L(\rho_{0})$ = 66.75$\pm$24.75 MeV is used. The calculations also clearly demonstrate that the high-momentum tail of the nucleon initialization in momentum space strongly affects the yields and ratios of pion production in Sn+Sn systems with different asymmetries near or below threshold. In addition, given many insoluble theoretical uncertainties in transport models, multi-system experimental measurements with various N/Z asymmetries are proposed to extract the symmetry energy less model-dependently by using heavy-ion collisions.

Impacts of nucleon-nucleon short-range correlations on neutron stars

Nucleon-nucleon short-range correlations (SRCs) are inevitable consequences of realistic nucleon-nucleon interactions. The corresponding SRC pairs, characterized by high relative momenta, have been verified experimentally to be important in finite nuclei. In this work, we study the impacts of nucleon-nucleon SRCs on the physical properties of neutron stars. Considering the small center-of-mass momenta of SRC pairs, new nucleon momentum distributions with high-momentum tails (HMTs) are proposed by extrapolating well-established experimental results of SRCs in finite nuclei to neutron star matter. HMTs with different shapes are adopted to estimate theoretical uncertainties. It is found that nucleon-nucleon SRCs generally stiffen the equation of state of neutron star matter and increase the maximum mass of neutron stars.

Neutron stars within a relativistic mean field theory compatible with nucleon-nucleon short-range correlations

Nucleon-nucleon short-range correlations (SRCs) result in the presence of high-momentum tail (HMT) above the Fermi surface in nucleon momentum distribution. In this work, we introduce HMT corrections in relativistic mean field (RMF) theory to make the theory compatible with the nucleon-nucleon SRCs. The properties of nucleonic stars and hyperon stars are studied within the RMF theory with HMT corrections. After introducing the HMT corrections, the equation of state (EoS) of the nucleonic star becomes softer and the maximum mass is smaller. The particle fractions of hyperon stars are significantly affected by the HMT corrections. The threshold densities of the presence of hyperons are changed dramatically. More importantly, with the introduction of HMT corrections, the mass-radius relations of nucleonic stars and hyperon stars can satisfy the stringent limits provided by the detection of gravitational wave.

Interplay of short-range correlations and nuclear symmetry energy in hard-photon production from heavy-ion reactions at Fermi energies

Within an isospin- and momentum-dependent transport model for nuclear reactions at intermediate energies, we investigate the interplay of the nucleon-nucleon short-range correlations (SRC) and nuclear symmetry energy $E_{sym}(\rho)$ on hard photon spectra in collisions of several Ca isotopes on $^{112}$Sn and $^{124}$Sn targets at a beam energy of 45 MeV/nucleon. It is found that over the whole spectra of hard photons studied, effects of the SRC overwhelm those due to the $E_{sym}(\rho)$. The energetic photons come mostly from the high-momentum tails (HMT) of single-nucleon momentum distributions in the target and projectile. Within the neutron-proton dominance model of SRC based on the consideration that the tensor force acts mostly in the isosinglet and spin-triplet nucleon-nucleon interaction channel, there are equal numbers of neutrons and protons, thus a zero isospin-asymmetry in the HMTs. Therefore, experimental measurements of the energetic photons from heavy-ion collisions at Fermi energies have the great potential to help us better understand the nature of SRC without any appreciable influence by the uncertain $E_{sym}(\rho)$. These measurements will be complementary to but also have some advantages over the ongoing and planned experiments using hadronic messengers from reactions induced by high-energy electrons or protons. Since the underlying physics of SRC and $E_{sym}(\rho)$ are closely correlated, a better understanding of the SRC will in turn help constrain the nuclear symmetry energy more precisely in a broad density range.

Nucleon-nucleon correlations, short-lived excitations, and the quarks within

This article reviews our current understanding of how the internal quark structure of a nucleon bound in nuclei differs from that of a free nucleon. We focus on the interpretation of measurements of the EMC effect for valence quarks, a reduction in the Deep Inelastic Scattering (DIS) cross-section ratios for nuclei relative to deuterium, and its possible connection to nucleon-nucleon Short-Range Correlations (SRC) in nuclei. Our review and new analysis (involving the amplitudes of non-nucleonic configurations in the nucleus) of the available experimental and theoretical evidence shows that there is a phenomenological relation between the EMC effect and the effects of SRC that is not an accident. The influence of strongly correlated neutron-proton pairs involving highly virtual nucleons is responsible for both effects. These correlated pairs are temporary high-density fluctuations in the nucleus in which the internal structure of the nucleons is briefly modified. This conclusion needs to be solidified by the future experiments and improved theoretical analyses that are discussed herein.

Modeling pion production in heavy-ion collisions at intermediate energies

Pion production in nucleus-nucleus collisions at intermediate energies was modeled in the framework of the Isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model. The effects of nucleon-nucleon short-range correlations in initialization and mean-field potential, isospin-dependent in-medium baryon-baryon elastic and inelastic cross sections and pion in-medium effect are all considered in this model. It is found that the ratio and yields of $\pi^{-}$and $\pi^{+}$ in Au+Au reaction at 400 MeV/nucleon reproduce the FOPI/GSI data very well especially with a soft symmetry energy in the present transport model. Predictions on the single and double $\pi^{-}/\pi^{+}$ ratio are made for the isotope reaction systems $^{132}\rm {Sn}+^{124}\rm {Sn}$ and $^{108}\rm {Sn}+^{112}\rm {Sn}$ at 300 MeV/nucleon since related experiments are being carried out at RIKEN/Japan.

Nuclear matrix element of neutrinoless double-βdecay: Relativity and short-range correlations

Background: The discovery of neutrinoless double-beta ($0\nu\beta\beta$) decay would demonstrate the nature of neutrinos, have profound implications for our understanding of matter-antimatter mystery, and solve the mass hierarchy problem of neutrinos. The calculations for the nuclear matrix elements $M^{0\nu}$ of $0\nu\beta\beta$ decay are crucial for the interpretation of this process. Purpose: We study the effects of relativity and nucleon-nucleon short-range correlations on the nuclear matrix elements $M^{0\nu}$ by assuming the mechanism of exchanging light or heavy neutrinos for the $0\nu\beta\beta$ decay. Methods: The nuclear matrix elements $M^{0\nu}$ are calculated within the framework of covariant density functional theory, where the beyond-mean-field correlations are included in the nuclear wave functions by configuration mixing of both angular-momentum and particle-number projected quadrupole deformed mean-field states. Results: The nuclear matrix elements $M^{0\nu}$ are obtained for ten $0\nu\beta\beta$-decay candidate nuclei. The impact of relativity is illustrated by adopting relativistic or nonrelativistic decay operators. The effects of short-range correlations are evaluated. Conclusions: The effects of relativity and short-range correlations play an important role in the mechanism of exchanging heavy neutrinos though the influences are marginal for light neutrinos. Combining the nuclear matrix elements $M^{0\nu}$ with the observed lower limits on the $0\nu\beta\beta$-decay half-lives, the predicted strongest limits on the effective masses are $|\langle m_\nu\rangle|<0.06~\mathrm{eV}$ for light neutrinos and $|\langle m_{\nu_h}^{-1}\rangle|^{-1}>3.065\times 10^8~\mathrm{GeV}$ for heavy neutrinos.

Universality of nucleon-nucleon short-range correlations: The factorization property of the nuclear wave function, the relative and center-of-mass momentum distributions, and the nuclear contacts

The two-nucleon momentum distributions have been calculated for nuclei up to A=40 and various values of the relative and center-of-mass momenta and angle between them. For complex nuclei a parameter-free linked-cluster expansion, based upon a realistic local two-nucleon interaction of the Argonne family and variational wave function featuring central, tensor, spin and iso-spin correlations, has been used. The obtained results show that: 1) independently of the mass number A, at values of the relative momentum k_rel> 2 fm^{-1} the proton-neutron momentum distributions for back-to-back (BB) nucleons (K_cm=0) exhibit the factorization property n_A^{pn}(k_rel,K_cm=0)=C_A^{pn} n_D(k_rel) n_{cm}^{pn}(K_cm=0), where n_D is the deuteron momentum distribution, n_{cm}^{pn}(K_{cm}=0) the momentum distribution of the c.m. motion of the pair and C_A^{pn} the nuclear contact measuring the number of BB pn pairs with deuteron-like momenta; 2) the values of the proton-neutron nuclear contact C_A^{pn} are obtained in a model-independent way from the ratio n_A^{pn}(k_rel,K_cm=0)/n_D(k_rel) n_{cm}^{pn}(K_cm=0); 3) also the K_cm-integrated pn momentum distributions divided by the deuteron momentum distribution exhibits a constant behavior equal to C_A^{pn}, but only at very high values of k_{rel}> 3.5fm^{-1}, where the relative momentum distribution is entirely governed by BB short-range correlated nucleons; 4) the absolute value of the number of pn and pp short-range correlated pairs is calculated, illustrating that the high values (K_cm>1 fm^{-1}) of the pair c.m. momentum appreciably reduce the dominance of the pn over pp pairs produced by the tensor force when K_cm=0; 5) calculations are in good agreement with the VMC calculations for light nuclei and with available experimental on the processes A(e,e'pn)X and A(e,e'pp)X.

UNIVERSALITY OF NUCLEON–NUCLEON SHORT-RANGE CORRELATIONS AND NUCLEON MOMENTUM DISTRIBUTIONS

By analyzing recent microscopic many-body calculations of few-nucleon systems and complex nuclei performed by different groups in terms of realistic nucleon–nucleon (NN) interactions, it is shown that NN short-range correlations (SRCs) have a universal character, in that the correlation hole that they produce in nuclei appears to be almost A-independent and similar to the correlation hole in the deuteron. The correlation hole creates high-momentum components, missing in a mean-field (MF) description and exhibiting several scaling properties and a peculiar spin–isospin structure. In particular, the momentum distribution of a pair of nucleons in spin–isospin state (ST) = (10), depending upon the pair relative (k rel ) and center-of-mass (c.m.) (K c.m. ) momenta, as well as upon the angle Θ between them, exhibits a remarkable property: in the region k rel ≳2 fm -1 and K c.m. ≲1 fm -1, the relative and c.m. motions are decoupled and the two-nucleon momentum distribution factorizes into the deuteron momentum distribution and an A-dependent momentum distribution describing the c.m. motion of the pair in the medium. The impact of these and other properties of one- and two-nucleon momentum distributions on various nuclear phenomena, on ab initio calculations in terms of low-momentum interactions, as well as on ongoing experimental investigations of SRCs, are briefly commented.

Comparison of forward and backwardpppair knockout in3He(e,e′pp)n

Measuring nucleon-nucleon Short Range Correlations (SRC) has been a goal of the nuclear physics community for many years. They are an important part of the nuclear wavefunction, accounting for almost all of the high-momentum strength. They are closely related to the EMC effect. While their overall probability has been measured, measuring their momentum distributions is more difficult. In order to determine the best configuration for studying SRC momentum distributions, we measured the $^3$He$(e,e'pp)n$ reaction, looking at events with high momentum protons ($p_p > 0.35$ GeV/c) and a low momentum neutron ($p_n< 0.2$ GeV/c). We examined two angular configurations: either both protons emitted forward or one proton emitted forward and one backward (with respect to the momentum transfer, $\vec q$). The measured relative momentum distribution of the events with one forward and one backward proton was much closer to the calculated initial-state $pp$ relative momentum distribution, indicating that this is the preferred configuration for measuring SRC.

Short-range nuclear effects on axion emissivities by nucleon–nucleon bremsstrahlung

The rates of axion emission by nucleon–nucleon (NN) bremsstrahlung are reconsidered by taking into account the NN short-range correlations. The analytical formulas for the neutron–neutron, proton–proton and neutron–proton processes with the inclusion of the full momentum dependence of one- and two-pion exchange nuclear potentials, in the non-degenerate limit, are explicitly given. We find that the two-pion exchange (short-range) effects can give a significant contribution to the emission rates, and are temperature dependent. Also, other short-range nuclear effects such as effective nucleon mass, polarization effects and use of correlated wave functions are discussed. The trend of all these nuclear effects is to diminish the corresponding axion emission rates. Furthermore, we estimate that the values of the emission rates calculated with the inclusion of all these effects can differ from the corresponding ones derived with constant nuclear matrix elements by a factor of ∼24. This leads to an uncertainty factor of ∼4.9 when extracting bounds of the axion parameters.

Universality of nucleon-nucleon short-range correlations: Two-nucleon momentum distributions in few-body systems

Using realistic wave functions, the proton-neutron and proton-proton momentum distributions in $^3He$ and $^4He$ are calculated as a function of the relative, $k_{rel}$, and center of mass, $K_{CM}$, momenta, and the angle between them. For large values of ${k}_{rel}\gtrsim 2\,\,fm^{-1}$ and small values of ${K}_{CM} \lesssim 1.0\,\,fm^{-1}$, both distributions are angle independent and decrease with increasing $K_{CM}$, with the $pn$ distribution factorizing into the deuteron momentum distribution times a rapidly decreasing function of $K_{CM}$, in agreement with the two-nucleon (2N) short range correlation (SRC) picture. When $K_{CM}$ and $k_{rel}$ are both large, the distributions exhibit a strong angle dependence, which is evidence of three-nucleon (3N) SRC. The predicted center-of-mass and angular dependence of 2N and 3N SRC should be observable in two-nucleon knock-out processes $A(e,e'pN)X$.

Quasifree scattering of electrons on light nuclei and some properties of nuclear interaction

The status of experimental and theoretical studies of the position of the quasifree cross-section maximum in the A(e, e′) reaction is discussed. The dependence of the shift of the maximum relative to the elastic eN-scattering on the kinematic conditions of measurements is considered. The possibilities of using the data for the selection of realistic models of nucleon-nucleon interaction and dynamic short-range correlations in nuclei, as well as for determining the parameters of the nucleon-nucleus potential and the nucleon effective mass, are analyzed.

NUCLEAR MATRIX ELEMENTS FOR DOUBLE BETA DECAY

The neutrinoless double beta (0νββ) decay of atomic nuclei plays a key role in the search for massive Majorana neutrinos and their mass scale. To extract the necessary information from the measured data the nuclear-structure effects have to be accounted for by computation of the associated nuclear matrix elements (NME's). In this article the NME's for the light-neutrino exchange mechanism are discussed. They are computed by using the proton-neutron quasiparticle random-phase approximation (pnQRPA). Recent developments in this field relate to the handling of the nucleon-nucleon short-range correlations and independent experimental probes of the wave functions relevant for the NME's.

Nuclear matrix elements of0νββdecay with improved short-range correlations

Nuclear matrix elements of the neutrinoless double beta ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decays of $^{96}\mathrm{Zr}$, $^{100}\mathrm{Mo}$, $^{116}\mathrm{Cd}$, $^{128}\mathrm{Te}$, $^{130}\mathrm{Te}$, and $^{136}\mathrm{Xe}$ are calculated for the light-neutrino exchange mechanism by using the proton-neutron quasiparticle random-phase approximation (pnQRPA) with a realistic nucleon-nucleon force. The particle-particle strength parameter ${g}_{\mathrm{pp}}$ of the pnQRPA is fixed by the data on the two-neutrino double \ensuremath{\beta} and single \ensuremath{\beta} decays. The finite size of a nucleon, the higher-order terms of nucleonic weak currents, and the nucleon-nucleon short-range correlations (s.r.c) are taken into account. The s.r.c. are computed by the traditional Jastrow method and by the more advanced unitary correlation operator method (UCOM). A comparison of the results obtained by the two methods reveals that the UCOM computed matrix elements are considerably larger than the Jastrow computed ones. This result is important to the assessment of the neutrino-mass sensitivity of present and future double \ensuremath{\beta} experiments.

Improved short-range correlations and0νββnuclear matrix elements ofGe76andSe82

We calculate the nuclear matrix elements of the neutrinoless double beta ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decays of $^{76}\mathrm{Ge}$ and $^{82}\mathrm{Se}$ for the light neutrino exchange mechanism. The nuclear wave functions are obtained by using realistic two-body forces within the proton-neutron quasiparticle random-phase approximation (pnQRPA). We include the effects that come from the finite size of a nucleon, from the higher-order terms of nucleonic weak currents, and from the nucleon-nucleon short-range correlations. Most importantly, we improve on the presently available calculations by replacing the rudimentary Jastrow short-range correlations by the more advanced unitary correlation operator method (UCOM). The UCOM-corrected matrix elements turn out to be notably larger in magnitude than the Jastrow-corrected ones. This has drastic consequences for the detectability of $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay in present and future double beta experiments.

Nuclear matter spectral function in the Bethe-Brueckner-Goldstone approach

The microscopic many-body theory of the Nuclear Equation of State is discussed in the framework of the Bethe-Brueckner-Goldstone method. The expansion is extended up to the three hole-line diagrams contribution. Within the same scheme, the hole spectral function is calculated in nuclear matter to assess the relevance of nucleon-nucleon short-range correlations. The calculation is carried out by using several nucleon-nucleon realistic interactions. Results are compared with other approaches based on variational methods and transport theory. Discrepancies appear in the high-energy region, which is sensitive to short-range correlations, and are due to the different many-body treatment more than to the specific NN interaction used. Both nuclear matter Equation of State and spectral function appear to be dominated by two-body correlations.

Nuclear matter hole spectral function in the Bethe–Brueckner–Goldstone approach

The hole spectral function is calculated in nuclear matter to assess the relevance of nucleon-nucleon short range correlations. The calculation is carried out within the Brueckner scheme of many-body theory by using several nucleon-nucleon realistic interactions. Results are compared with other approaches based on variational methods and transport theory. Discrepancies appear in the high energy region, which is sensitive to short range correlations, and are due to the different many-body treatment more than to the specific N-N interaction used. Another conclusion is that the momentum dependence of the G-matrix should be taken into account in any self consistent approach.