Pion Exchange Potential Research Articles

The spin-current tensor contribution in collision dynamics

Spin polarization, which arises mostly from the spin-orbit force, spontaneously takes place in the early stage of heavy-ion reactions, and affects the equilibration process to a large extent. On the other hand, the tensor force, whose origin can be found in the one pion exchange potential, has been shown to play a crucial role in nuclear structure. In this paper, based on time-dependent density functional calculations, the difference between spin-orbit and spin-current tensor contributions is shown in the dynamics of low-energy heavy-ion collisions.

Study of Deuteron with Modified Screen Coulomb (Yakawa) Potential

In this paper the Schrodinger equation was solved with modified screen coulomb (yukawa) potential and the one pion exchange potential. A mathematical method has been presented. Analytical solution of the Schrödinger equation with modified yukawa potential has been calculated. Then the ground state energy of deuteron was determined. We have used the second potential as a perturbation potential and found the energy shift of grand state energy of deuteron. Then we have used numerical method and solving the Schrödinger equation numerically. Finally, the results were compared with Bonn group and the HQCD.

Exotic nuclei with charm and bottom flavor

We discuss the possibility of existence of exotic nuclei containing charm and bottom mesons. We study the interaction between (B) mesons and nucleons from view of heavy quark symmetry, and derive the one pion exchange potentials. We apply these potentials to the two body system of (B) meson and nucleon N , and find there are possible stable bound states with spin JP = 1/2− and isospin I = 0. We find that the tensor interaction mixing N and *N (BN and B*N) plays an important role. We also qualitatively discuss the possible bound states of (B) meson and two nucleons.

Addendum to “Pion mass effects on axion emission from neutron stars through NN bremsstrahlung processes” [Nucl. Phys. A 828 (2009) 439–449

The rates of axion emission by nucleon-nucleon bremsstrahlung are calculated with the inclusion of the full momentum contribution from a nuclear one pion exchange (OPE) potential. The contributions of the neutron-neutron (nn), proton-proton (pp) and neutron-proton (np) processes in both the nondegenerate and degenerate limits are explicitly given. We find that the finite momentum corrections to the emissivities are quantitatively significant for the non-degenerate regime and temperature-dependent, and should affect the existing axion mass bounds. The trend of these nuclear effects is to diminish the emissivities.

Pion mass effects on axion emission from neutron stars through NN bremsstrahlung processes

The rates of axion emission by nucleon–nucleon bremsstrahlung are calculated with the inclusion of the full momentum contribution from a nuclear one pion exchange (OPE) potential. The contributions of the neutron–neutron ( nn), proton–proton ( pp) and neutron–proton ( np) processes in both the non-degenerate and degenerate limits are explicitly given. We find that the finite-momentum corrections to the emissivities are quantitatively significant for the non-degenerate regime and temperature-dependent, and should affect the existing axion mass bounds. The trend of these nuclear effects is to diminish the emissivities.

Is X(3872) really a molecular state?

After taking into account both the pion and sigma meson exchange potential, we have performed a dynamical calculation of the D-0(D) over bar*(0) system. The s meson exchange potential is repulsive from heavy quark symmetry and numerically important for a loosely bound system. Our analysis disfavors the interpretation of X(3872) as a loosely bound molecular state if we use the experimental D*D pi coupling constant g = 0.59 and a reasonable cutoff around 1 GeV, which is the typical hadronic scale. Bound state solutions with negative eigenvalues for the D-0(D) over bar* system exist only with either a very large coupling constant (twice the experimental value) or a large cutoff (Lambda similar to 6GeV or beta similar to 6GeV(2)). In contrast, there probably exists a loosely bound S-wave B (B) over bar* molecular state. Once produced, such a molecular state would be rather stable, since its dominant decay mode is the radiative decay through B* -> B gamma. Experimental search of these states will be very interesting.

Z+(4430)as aD1′D*(D1D*) molecular state

We reexamine whether Z(+)(4430) could be a D(1)'-D* or D(1)-D* molecular state after considering both the pion and sigma meson exchange potentials and introducing the form factor to take into account the structure effect of the interaction vertex. Our numerical analysis with Matlab package MATSLISE indicates the contribution from the sigma meson exchange is small for the D(1)'-D* system and significant for the D(1)-D* system. The S-wave D(1)-(D) over bar* molecular state with only J(P)=0(-) and D(1)'-D* molecular states with J(P)=0(-),1(-),2(-) may exist with reasonable parameters. One should investigate whether the broad width of D(1)' disfavors the possible formation of molecular states in the future. The bottom analog Z(B) of Z(+)(4430) has a larger binding energy, which may be searched at Tevatron and LHC. Experimental measurement of the quantum number of Z(+)(4430) may help uncover its underlying structure.

Renormalization group analysis of boundary conditions in potential scattering

We analyze how a short distance boundary condition for the Schrödinger equation must change as a function of the boundary radius by imposing the physical requirement of phase shift independence on the boundary condition. The resulting equation can be interpreted as a variable phase equation of a complementary boundary value problem. We discuss the corresponding infrared fixed points and the perturbative expansion around them generating a short distance modified effective range theory. We also discuss ultraviolet fixed points, limit cycles, and attractors with a given fractality which take place for singular attractive potentials at the origin. The scaling behavior of scattering observables can analytically be determined and is studied with some emphasis on the low energy nucleon–nucleon interaction via singular pion exchange potentials. The generalization to coupled channels is also studied.

SCALING LIMIT FOR A GENERALIZATION OF THE NELSON MODEL AND ITS APPLICATION TO NUCLEAR PHYSICS

We study a mathematically rigorous derivation of a quantum mechanical Hamiltonian in a general framework. We derive such a Hamiltonian by taking a scaling limit for a generalization of the Nelson model, which is an abstract interaction model between particles and a Bose field with some internal degrees of freedom. Applying it to a model for the field of the nuclear force with isospins, we obtain a Schrödinger Hamiltonian with a matrix-valued potential, the one pion exchange potential, describing an effective interaction between nucleons.

Renormalization of the deuteron with one pion exchange

We analyze the deuteron bound state through the one pion exchange potential. We pay attention to the short distance peculiar singularity structure of the bound state wave functions in coordinate space and the elimination of short distance ambiguities by selecting the regular solution at the origin. We determine the so far elusive amplitude of the converging exponential solutions at the origin. All bound state deuteron properties can then be uniquely deduced from the deuteron binding energy, the pion-nucleon coupling constant, and pion mass. This generates correlations among deuteron properties. Scattering phase shifts and low energy parameters in the ${}^{3}{S}_{1}\text{\ensuremath{-}}{}^{3}{D}_{1}$ channel are constructed by requiring orthogonality of the positive energy states to the deuteron bound state, yielding an energy independent combination of boundary conditions. We also analyze from the viewpoint of short distance boundary conditions the weak binding regime on the light of long distance perturbation theory and discuss the approach to the chiral limit.

Time-reversal-violating Schiff moment ofHg199

We calculate the Schiff moment of the nucleus $^{199}\mathrm{Hg}$, created by \ensuremath{\pi}NN vertices that are odd under parity (P) and time-reversal (T). Our approach, formulated in diagrammatic perturbation theory with important core-polarization diagrams summed to all orders, gives a close approximation to the expectation value of the Schiff operator in the odd-A Hartree-Fock-Bogoliubov ground state generated by a Skyrme interaction and a weak P- and T-odd pion-exchange potential. To assess the uncertainty in the results, we carry out the calculation with several Skyrme interactions, the quality of which we test by checking predictions for the isoscalar-$E1$ strength distribution in $^{208}\mathrm{Pb}$, and estimate most of the important diagrams we omit.

On the existence of heavy pentaquarks: The largeNcand heavy quark limits and beyond

We present a very general argument that the analogue of a heavy pentaquark (a state with the quantum numbers of a baryon combined with an additional light quark and a heavy antiquark $\overline{Q}$) must exist as a particle stable under strong interactions in the combined heavy quark and large ${N}_{c}$ limits of QCD. Moreover, in the combined limit these heavy pentaquark states fill multiplets of $\mathrm{SU}(4)\ifmmode\times\else\texttimes\fi{}\mathrm{O}(8)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$. We explore the question of whether corrections in the combined $1/{N}_{c}$ and $1/{m}_{Q}$ expansions are sufficiently small to maintain this qualitative result. Since no model-independent way is known to answer this question, we use a class of realistic hadronic models in which a pentaquark can be formed via nucleon-heavy-meson binding through a pion-exchange potential. These models have the virtue that they necessarily yield the correct behavior in the combined limit, and the long-distance parts of the interactions are model independent. If the long-distance attraction in these models were to predict bound states in a robust way (i.e., largely insensitive to the details of the short-range interaction), then one could safely conclude that heavy pentaquarks do exist. However, in practice the binding does depend very strongly on the details of the short-distance physics, suggesting that the real world is not sufficiently near the combined large ${N}_{c}$, ${m}_{Q}$ limit to use it as a reliable guide. Whether stable heavy pentaquarks exist remains an open question.

Renormalization ofNNscattering with one pion exchange and energy dependent boundary conditions

A nonperturbative renormalization scheme for nucleon-nucleon interaction based on boundary conditions at short distances is presented and applied to the one pion exchange potential. It is free of off-shell ambiguities and ultraviolet divergences, provides finite results at any step of the calculation, and allows us to remove the short distance cutoff in a suitable way. Low energy constants and their nonperturbative evolution can be directly obtained from experimental threshold parameters in a completely unique and model independent way when the long range explicit pion effects are eliminated. This allows us to compute scattering phase shifts which are, by construction, consistent with the effective range expansion to a given order in the center of mass (c.m.) momentum $p$. In the singlet $^{1}S_{0}$ and triplet $^{3}S_{1}\text{\ensuremath{-}}^{3}D_{1}$ channels ultraviolet fixed points and limit cycles are obtained, respectively, for the threshold parameters. Data are described satisfactorily up to c.m. momenta of about $p\ensuremath{\sim}{m}_{\ensuremath{\pi}}$.

Nuclear effects on neutrino emissivities from nucleon-nucleon bremsstrahlung

The rates of neutrino pair emission by nucleon-nucleon (NN) bremsstrahlung are calculated with the inclusion of the full contribution from a nuclear one pion exchange potential (OPEP). We compute the contributions from the neutron-neutron (nn), proton-proton (pp), and neutron-proton (np) processes for physical conditions encountered in supernovae and neutron stars, both in the degenerate (D) and nondegenerate (ND) limits. We find a significant reduction of these rates, especially for the nn and pp processes, in comparison with the case when the whole nuclear contribution was replaced by constants, representing the high-momentum limits of the expressions of the nuclear potential. Furthermore, we also perform the calculations by including contributions due to the $\ensuremath{\rho}$ meson exchange between nucleons, in the OPEP. This may be relevant for processes produced in the inner core of neutron stars, where the density may exceed several times the standard nuclear density, and the short-range part of the NN interaction should be taken into account. These corrections lead to an additional suppression of the neutrino emission rates between (8 and 36)%, depending on the process [nn (pp) or np] and physical conditions (temperature and degeneracy of the nucleons).

Renormalization of singlet NN-scattering with one pion exchange and boundary conditions

We present a simple and physically compelling boundary condition regularization scheme in the framework of effective field theory as applied to nucleon–nucleon interaction. It is free of off-shell ambiguities and ultraviolet divergences and provides finite results at any step of the calculation. Low-energy constants and their non-perturbative evolution can directly be obtained from experimental threshold parameters in a completely unique, one-valued and model independent way when the long range explicit pion effects are removed. This allows to compute scattering phase shifts which are, by construction consistent with effective range expansion to a given order in the CM momentum and are free from finite cut-off artifacts. We illustrate how the method works in the 1S0 channel for the one pion exchange potential.

Renormalizing the Lippmann-Schwinger equation for the one-pion exchange potential

We address the question whether the cut-off dependence, which has to be introduced in order to properly define the Lippmann-Schwinger equation for the one pion exchange potential plus local (delta-function) potentials, can be removed (up to inverse powers of it) by a suitable tuning of the various (bare) coupling constants. We prove that this is indeed so both for the spin singlet and for the spin triplet channels. However, the latter requires such a strong cut-off dependence of the coupling constant associated to the non-local term which breaks orbital angular momentum conservation, that the renormalized amplitude lacks from partial wave mixing. We argue that this is an indication that this term must be treated perturbatively.

Coherent pair state of the pion in the constituent quark model

A coherent state of pions is introduced to the nonrelativistic quark model. The coherent pair approximation is employed for the pion field in order to maintain the spin-isospin symmetry. In this approximation the pion is localized in the momentum space, and the vertex form factor in the pion-quark interaction is derived from this localization. The nucleon masses and wave functions are calculated using this model, and our results are compared to those of the quark model with the one pion exchange potential. Similar result is obtained for the mass spectrum, but there exists a clear difference in the internal structure of nucleon resonances.

Relativistic description of constituent quarks

In this paper we propose a formalism to remove the center of mass motion of the relativistic three-quark system in order to calculate not only one-body operators, but also two-body interactions. We employ various methods used in the past to remove the center of mass motion. We then calculate the masses of the nucleon and \ensuremath{\Delta} resonance with residual one-gluon, sigma meson, and pseudoscalar pion and eta meson exchange potentials. Magnetic moments, root mean square radii, pion-nucleon coupling constant, and the axial vector coupling constant are also calculated. The main purpose of the calculation is to study the effect of the removal of the center of mass motion and investigate the similarities and differences between a relativistic and nonrelativistic description of constituent quarks. The method projecting onto the total momentum $P=0,$ is found to give results consistent with experiments. It is also found that light quark mass and strong confinement are appropriate to reproduce the nucleon and \ensuremath{\Delta} masses in the relativistic approach.

Nucleon-nucleon scattering and effective field theory: including pions non-perturbatively

Next to leading order effective field theory calculations are performed for 1S 0 NN scattering using subtractive renormalization procedure. One pion exchange and contact interaction potentials are iterated using Lippman-Schwinger equation. Satisfactory fit to the Nijmegen data is obtained for the momenta up to 300 MeV in the centre of mass frame. Phase shifts are also compared with the results of KSW approach where pions are included perturbatively.

Variational calculations of the Lambda -separation energy of the Lambda 17O hypernucleus.

Variational Monte Carlo calculations have been made for the $_{ \Lambda}^{17}$O hypernucleus using realistic two- and three-baryon interactions. A two pion exchange potential with spin- and space-exchange components is used for the $\Lambda$N potential. Three-body two-pion exchange and strongly repulsive dispersive $\Lambda$NN interactions are also included. The trial wave function is constructed from pair- and triplet-correlation operators acting on a single particle determinant. These operators consist of central, spin, isospin, tensor and three- baryon potential components. A cluster Monte Carlo method is developed for noncentral correlations and is used with up to four-baryon clusters in our calculations. The three-baryon $\Lambda$NN force is discussed.