Two- and three- particles photodisintegration of the triton is investigated in a three-dimensional (3D) Faddeev approach. For this purpose the Jacobi momentum vectors for three particles system and spin-isospin quantum numbers of the individual nucleons are considered. Based on this picture the three-nucleon Faddeev integral equations with the two-nucleon interaction are formulated without employing the partial wave decomposition. The single nucleon current as well as $π-$ and $ρ-$ like exchange currents are used in an appropriate form to be employed in 3D approach. The exchange currents are derived from AV18 NN force. The two-body t-matrix, Deuteron and Triton wave functions are calculated in the 3D approach by using AV18 potential. Benchmarks are presented to compare the total cross section for the two- and three- particles photodisintegration in the range of $E_γ<30 MeV$. The 3D Faddeev approach shows promising results.
The photodisintegration of $^{3}$H is treated by means of coupled integral equations using separable versions of the Paris and the Bonn potentials in their kernel. The differential cross section for the inverse reaction is obtained via detailed balance. For the latter process good agreement with the data is found when including final-state interaction, meson exchange currents, higher partial waves in the potential, and electric quadrupole contributions in the electromagnetic interaction.
The process $γ+ t \to n + d$ is treated by means of three-body integral equations employing in their kernel the W-Matrix representation of the subsystem amplitudes. As compared to the plane wave (Born) approximation the full solution of the integral equations, which takes into account the final state interaction, shows at low energies a 24% enhancement. The calculations are based on the semirealistic Malfliet-Tjon and the realistic Paris and Bonn B potentials. For comparison with earlier calculations we also present results for the Yamaguchi potential. In the low-energy region a remarkable pot…
Effective field theory (EFT) has been recently used for the calculation of neutron-deuteron radiative capture at very low energies.We present here the use of EFT to calculate the two-body photodisintegration of the triton, considering the three-body force. The calculated cross section shows sharp rising from threshold to maximum about 0.88 mb at 13 MeV and decreasing slightly to about 0.81 mb at 19 MeV, in agreement with the experimental data. Our results are in good agreement with the experimental data and the other calculations using modern realistic two- and three-nucleon forces, like AV18/…
An interaction of a photon with $^3H$ is invstigated based on a three dimensional Faddeev approach. In this approach the three-nucleon Faddeev equations with two-nucleon interactions are formulated with consideration of the magnitude of the vector Jacobi momenta and the angle between them with the inclusion of the spin-isospin quantum numbers, without employing a partial wave decomposition. In this formulation the two body t-matrices and triton wave function are calculated in the three dimensional approach using AV18 potential. In the first step we use the standard single nucleon current in th…
A benchmark is set on the three-nucleon photodisintegration calculating the total cross section with modern realistic two- and three-nucleon forces (AV18, UrbIX) using both the Faddeev equations and the Lorentz Integral Transform method. This test shows that the precision of three-body calculations involving continuum states is considerably higher than experimental uncertainties. Effects due to retardations, higher multipoles, meson exchange currents and Coulomb force are studied.
The total photodisintegration cross sections of three-body nuclei are calculated with semirealistic NN potentials below pion threshold. Full final state interaction with Coulomb force is taken into account via the Lorentz integral transform method. The experimental total cross sections are well described and the sum rule $σ_{-1}(^3$H) agrees with elastic electron scattering data. The calculated ^3He polarizability is 0.15 fm^3.
Faddeev calculations have been performed for nucleon-deuteron photodisintegration of 3He(3H) and proton-deuteron radiative capture. The bulk of the results is based on the AV18 nucleon-nucleon force and the Urbana IX three-nucleon force together with explicit exchange currents or applying the Siegert approach. Three-nucleon force effects are predicted for both processes and supported by most of the data.
The three-nucleon photodisintegration of 3He has been calculated in the whole phase space using consistent Faddeev equations for the three-nucleon bound and scattering states. Modern nucleon-nucleon and 3N forces have been applied as well as different approaches to nuclear currents. Phase space regions are localized where 3N force effects are especially large. In addition semi-exclusive cross sections for 3He(gamma,N) have been predicted which carry interesting peak structures. Finally some data for the exclusive 3N breakup process of 3He and its total breakup cross section have been compared …
Different momentum space Faddeev-like equations and their solutions for the radiative pd-capture and the three-nucleon photodisintegration of 3He are presented. Applications are based on the AV18 nucleon-nucleon and the Urbana IX three nucleon forces. Meson exchange currents are included using the Siegert theorem. A very good agreement has been found in all cases indicating the reliability of the used numerical methods. Predictions for cross sections and polarization observables in the pd-capture and the complete three nucleon breakup of 3He at different incoming deuteron/photon energies are p…
We focus on a characteristic non-alpha cluster structure in light neutron-rich nuclei; three triton structure in 9Li. This is an analogy to the case of three alpha state in 12C (Hoyle state). The alpha clusters behave as bosons. however tritons have Fermionic nature, and how the three cluster structure is different from 12C is an intriguing problem. For this purpose, we introduce three triton wave functions. In addition, alpha+t+n+n wave functions are prepared to describe other low-lying states of 9Li, and the coupling effect between them is taken into account. The states with dominantly the t…
The photodisintegration of $^9$Be in the energy region lower than $E_γ= 16$ MeV is investigated by using the $α$~+~$α$~+~$n$ three-body model and the complex scaling method. The cross section exhibits two aspects in the different two energy regions. In the low energy region up to $E_γ= 6$ MeV, the cross section is explained by the transition strengths into the excited resonant states of $^9$Be, while the dipole transition into the non-resonant continuum states of $^8$Be(2$^+$)~+~$n$ dominates the cross section in the energy region of $6 \le E_γ\le 16$ MeV. Furthermore, it is shown that the dip…
We use a microscopic three-cluster model with the $α+α+n$ configuration to analyze with astrophysical interests the photodisintegration cross section of $^9$Be. The valence neutron in $^9$Be is treated in the molecular orbit model (MO), including continuum states by the box discretization method. It is shown that good agreement is achieved with the recently measured B(E1) transition probability from the ground state to the first 1/2$^+$ state when the box size is enlarged, resulting in reasonable reproduction of the experimental data for the photodisintegration cross section. The Coulomb disso…
Long-range contributions to the three-nucleon force that have been recently worked out in chiral effective field theory at next-to-next-to-next-to-leading order are for the first time included in the triton and the doublet nucleon-deuteron scattering length calculations. The strengths of the two short-range terms available at this order in the chiral expansion are determined from the triton binding energy and the neutron-deuteron doublet scattering length. The structure of the resulting three-nucleon force is explored and effects for the two-nucleon correlation function in the triton are inves…
The cross sections of the processes $^4$He($γ,p$)$^3$H and $^4$He($γ,n$)$^3$He are calculated taking into account the full final state interaction via the Lorentz integral transform (LIT) method. This is the first consistent microscopic calculation beyond the three--body breakup threshold. The results are obtained with a semirealistic central NN potential including also the Coulomb force. The cross sections show a pronounced dipole peak at 27 MeV which lies within the rather broad experimental band. At higher energies, where experimental uncertainties are considerably smaller, one finds a good…
We present high precision benchmark calculations for the triton binding energy using the most recent, phase equivalent realistic nucleon-nucleon (NN) potentials and the Tuscon-Melbourne pi-pi three-nucleon force (3NF). That 3NF is included with partial waves up to a total two-body angular momentum of j_max=6. It is shown that the inclusion of the 3NF slows down the convergence in the partial waves and j_max=5 is needed in order to achieve converged results within a few keV. We adjust the cut-off parameter Lambda in the form factors of the Tuscon-Melbourne 3NF separately for the different NN po…
The Faddeev equations are solved in momentum space for the trinucleon bound state with the new Tucson-Melbourne $π$ and $ρ$ exchange three-nucleon potentials. The three-nucleon potentials are combined with a variety of realistic two-nucleon potentials. The dependence of the triton binding energy on the $πNN$ cut-off parameter in the three-nucleon potentials is studied and found to be reduced compared to the case with pure $π$ exchange. The $ρ$ exchange parts of the three-nucleon potential yield an overall repulsive effect. When the recommended parameters are employed, the calculated triton bin…
Three- and four-nucleon photodisintegration processes are quite efficiently treated by means of effective two-body integral equations in momentum space. We recall some aspects of their derivation, present previous and most recent results obtained within this framework, and discuss general features, trends and effects observed in these investigations: At low energies final-state interaction plays an important role. Even more pronounced is the effect of meson exchange currents. A considerable potential dependence shows up in the low-energy peak region. The different peak heights are found to be …
We apply the effective field theory approach to the three-nucleon system. In particular, we consider neutron-deuteron scattering and the triton. Precise predictions for S=3/2 scattering are obtained in a straightforward way. In the S=1/2 channel, however, a unique nonperturbative renormalization takes place which requires the introduction of a three-body force at leading order. We also show that invariance under the renormalization group explains some universal features of the three-nucleon system.
We extend and systematise the power counting for the three-body system, in the context of the ``pion-less'' Effective Field Theory approach, to all orders in the low-energy expansion. We show that a sub-leading part of the three-body force appears at the third order and delineate how the expansion proceeds at higher orders. After discussing the renormalisation issues in a simple bosonic model, we compute the phase shifts for neutron-deuteron scattering in the doublet S wave (triton) channel and compare our results with phase shift analysis and potential model calculations.
The ${}^9$Be photodisintegration cross section within Cluster Effective Field Theory
Università del Salento（莱切萨伦托大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Lecce（意大利国家核物理研究所莱切分部）；European Center for Theoretical Studies in Nuclear Physics and Related Areas (ECT*)（欧洲核物理及相关领域理论研究中心）；INFN-TIFPA Trento Institute of Fundamental Physics and Applications（特伦托基础物理及其应用研究所）；Central China Normal University（华中师范大学）；Università di Trento（特伦托大学）
We apply the effective field theory approach to the three-nucleon system. In particular, we consider S=1/2 neutron-deuteron scattering and the triton. We show that in this channel a unique nonperturbative renormalization takes place which requires the introduction of a single three-body force at leading order. With one fitted parameter we find a good description of low-energy data. Invariance under the renormalization group explains some universal features of the three-nucleon system ---such as the Thomas and Efimov effects and the Phillips line--- and the origin of SU(4) symmetry in nuclei.
Triton properties are calculated using new nucleon-nucleon potentials, which were fit to the world nucleon-nucleon data. All potentials are charge dependent and explicitly incorporate the mass difference between the charged and neutral pions. Three of these models have a nearly optimal chi**2 per degree of freedom and can therefore be considered as alternative partial wave analyses, which in quality can almost compete with the Nijmegen partial-wave analysis. The triton binding energy obtained with three local models (Nijm II, Reid93, AV18) can be summarized as 7.62 +_ 0.01 MeV, which is nearly…
Determination of the proper power-counting scheme is an important issue for the systematic application of Chiral Effective Field Theory in nuclear physics. We analyze the cutoff dependence of three-nucleon observables (the neutron-deuteron scattering lengths and the triton binding energy) at the leading and next-to-leading orders of a power counting that ensures order-by-order renormalization in the two-nucleon system. Our results imply that three-body forces are not needed for renormalization of the three-nucleon system up to next-to-leading order, as usually assumed in the literature. (Errat…
Total photonuclear absorption cross sections of $^3$H and $^3$He are studied using realistic NN and NNN forces. Final state interactions are fully included. Two NN potential models, the AV14 and the r-space Bonn-A potentials, are considered. For the NNN forces the Urbana-VIII and Tucson-Melbourne models are employed. We find the cross section to be sensitive to nuclear dynamics. Of particular interest in this work is the effect which NNN forces have on the cross section. The addition of NNN forces not only lowers the peak height but increases the cross section beyond 70 MeV by roughly 15%. Cro…
For relativistic three-body calculations, essentially two different approaches are in use: field theory and relativistic direct interactions. Results for relativistic corrections of the triton binding energy obtained from the two approaches differ even in their sign, which is rather puzzling. In this paper, we discuss the origin of such discrepancy. We show that the use of an invariant two-body amplitude, as done in the field-theoretic approach, increases the triton binding energy by about 0.30 MeV. This may explain a large part of the discrepancy.
Proton-deuteron radiative capture and two- and three-body photodisintegration of 3He at low energy are described using realistic hadronic dynamics and including the Coulomb force. The sensitivity of the observables to the relativistic corrections of one-nucleon electromagnetic current operator is studied. Significant effects of the relativistic spin-orbit charge are found for the vector analyzing powers in the proton-deuteron radiative capture and for the beam-target parallel-antiparallel spin asymmetry in the three-body photodisintegration of 3He.
The three-nucleon bound state problem is studied employing nucleon-nucleon potentials derived from a basic quark-quark interaction. We analyze the effects of the nonlocalities generated by the quark model. The calculated triton binding energies indicate that quark-model nonlocalities can yield additional binding in the order of few hundred keV.
Photodisintegration of polarized 3He by linearly or circularily polarized photons offers a rich choice of observables which can be calculated with high precision using a rigorous scheme of three-nucleon Faddeev equations. Using the (semi)phenomenological AV18 nucleon-nucleon potential combined with the Urbana IX three-nucleon force we investigate sensitivity of 3He photodisintegration observables to underlying currents taken in the form of a single-nucleon current supplemented by two-body contributions for $π$- and $ρ$-meson exchanges or incorporated by the Siegert theorem. Promising observabl…
As an application of the new realistic three-dimensional (3D) formalism reported recently for three-nucleon (3N) bound states, an attempt is made to study the effect of three-nucleon forces (3NFs) in triton binding energy in a non partial wave (PW) approach. The spin-isospin dependent 3N Faddeev integral equations with the inclusion of 3NFs, which are formulated as function of vector Jacobi momenta, specifically the magnitudes of the momenta and the angle between them, are solved with Bonn-B and Tucson-Melbourne NN and 3N forces in operator forms which can be incorporated in our 3D formalism. …
Making use of the Effective Field Theory(EFT) expansion recently developed by the authors, we compute the charge form factor of triton up to next-to-next-to-leading order (N$^2$LO). The three-nucleon forces(3NF) is required for renormalization of the three-nucleon system and it effects are predicted for process and is qualitatively supported by available experimental data. We also show that, by including higher order corrections, the calculated charge form factor and charge radius of $^3$H are in satisfactory agreement with the experimental data and the realistic Argonne $v_{18}$ two-nucleon a…
We report 3H binding energy calculations using inversion potentials generated from phase shifts corresponding to contemporary nucleon-nucleon potentials as well as modern phase shift analyses. We place limits upon local potential triton binding energy calculations due to the underlying uncertainties in their fit to the nucleon-nucleon phase shifts: 7.7 +/- 0.2 MeV. We explore the role of the nonlocality of momentum dependent potentials in the triton binding energy. In particular, we find the additional binding energy in the case of the Bonn-B potential is due to a long range nonlocality, which…
The influence of the partial-wave states with nonzero orbital moment of the nucleon pair on the binding energy of the triton in the relativistic case is considered. The relativistic generalization of the Faddeev equation in the Bethe-Salpeter formalism is applied. Two-nucleon t matrix is obtained from the Bethe-Salpeter equation with separable kernel of nucleon-nucleon interaction of the rank one. The kernel form factors are the relativistic type of the Yamaguchi functions. The following two-nucleon partial-wave states are considered: $^1S_0$, $^3S_1$, $^3D_1$, $^3P_0$, $^1P_1$, $^3P_1$. The s…
Previously we calculated the binding energies of the triton and hypertriton, using an SU_6 quark-model interaction derived from a resonating-group method of two baryon clusters. In contrast to the previous calculations employing the energy-dependent interaction kernel, we present new results using a renormalized interaction, which is now energy independent and reserves all the two-baryon data. The new binding energies are slightly smaller than the previous values. In particular the triton binding energy turns out to be 8.14 MeV with a charge-dependence correction of the two-nucleon force, 190 …
In nuclear physics, triton and helium-3 nucleus can be understood as three-body hadronic molecules. Analogous to the loosely bound structures for the triton and helium-3 nucleus, whether there is a bound state formed by three hadrons leaves us an open issue. Based on the one-boson exchange model as well as the adoption of the variational approach, we make a comprehensive investigation on the tritonlike systems of three identical baryons $NNN$, $ΛΛΛ$, $ΞΞΞ$ and $ΣΣΣ$. We predict that the three-body molecular states for the systems of three identical hadrons of baryon octet are probably existent…
We consider the three-nucleon system within an effective theory with contact interactions at leading order in the large scattering length. We calculate the charge form factor of the triton at low momentum transfer and extract the triton charge radius. At this order, no two-body currents contribute and the calculation can be performed in the impulse approximation. We also comment on the power counting for higher orders. The requirement of a three-body force for renormalization of the three-nucleon system explains the previously observed correlation between the triton binding energy and charge r…
A simple analytical expression for the electric dipole polarizability of the three-hadron bound system having only one stable bound state has been derived neglecting by the higher orbital components of the off-shell three-body transition matrix at the energy of the bound state. As a case in point, we have estimated the electric dipole polarizability of the triton, using a cluster triton wave function and the Hulthen potential to describe the related p-n and n-d bound states.
3He and the triton are studied as three-body bound states in the effective field theory without pions. We study 3He using the set of integral equations developed by Kok et al. which includes the full off-shell T-matrix for the Coulomb interaction between the protons. To leading order, the theory contains: two-body contact interactions whose renormalized strengths are set by the NN scattering lengths, the Coulomb potential, and a three-body contact interaction. We solve the three coupled integral equations with a sharp momentum cutoff, Lambda, and find that a three-body interaction is required …
We introduce new values of the strength constants (i.e., $a$, $b$, $c$, and $d$ coefficients) of the Tucson-Melbourne (TM) 2$π$ exchange three nucleon potential. The new values come from contemporary dispersion relation analyses of meson factory $π$N scattering data. We make variational Monte Carlo calculations of the triton with the original and updated three-body forces to study the effects of this update. We remove a short-range -- $π$-range part of the potential due to the $c$ coefficient and discuss the effect on the triton binding energy.
Properties of the three-nucleon bound state are examined in the Faddeev formalism, in which the quark-model nucleon-nucleon interaction is explicitly incorporated to calculate the off-shell T-matrix. The most recent version, fss2, of the Kyoto-Niigata quark-model potential yields the ground-state energy ^3H=-8.514 MeV in the 34 channel calculation, when the np interaction is used for the nucleon-nucleon interaction. The charge root mean square radii of the ^3H and ^3He are 1.72 fm and 1.90 fm, respectively, including the finite size correction of the nucleons. These values are the closest to t…
The well-known correlations of low-energy three and four-nucleon observables with a typical three-nucleon scale (e.g., the Tjon line) is extended to light nuclei and nuclear matter. Evidence for the scaling between light nuclei binding energies and the triton one are pointed out. We argue that the saturation energy and density of nuclear matter are correlated to the triton binding energy. The available systematic nuclear matter calculations indicate a possible band structure representing these correlations.
The three-nucleon bound state problem is studied employing a nucleon-nucleon potential obtained from a basic quark-quark interaction in a five-channel Faddeev calculation. The obtained triton binding energy is comparable to those predicted by conventional models of the $NN$ force.
The effect of nucleon dressing by pions, on the binding energy of three nucleons interacting via two-body forces, is calculated for the first time within a conventional nuclear physics approach. It is found that the dressing increases the binding energy of the triton by an amount approximately in the range from 0.3 MeV to 0.9 MeV, depending on the model used for dressing. This suggests that nucleon dressing may help explain the underestimation of the triton binding energy in previous calculations using only two-nucleon forces.
We study the triton and three-nucleon force at lowest chiral order in pionless effective field theory both in the Hamiltonian and Euclidean nuclear lattice formalism. In the case of the Euclidean lattice formalism, we derive the exact few-body worldline amplitudes corresponding to the standard many-body lattice action. This will be useful for setting low-energy coefficients in future nuclear lattice simulations. We work in the Wigner SU(4)-symmetric limit where the S-wave scattering lengths {1}S{0} and {3}S{1} are equal. By comparing with continuum results, we demonstrate for the first time th…
The emergence of Efimov levels in a three-body system is investigated near the unitarity limit characterized by resonating two-body interaction. No direct evidence of Efimov levels is seen in the three-nucleon system since the triton is the only physical bound state. We provide a model-independent analysis of nucleon-deuteron scattering at low energy by formulating a consistent effective field theory. We show that virtual states evolve into shallow bound states, which emerge as excited triton levels as we drive the system towards unitarity. Even though we consider this specific system, our res…
We discuss the available data for the differential and the total cross section for the photodisintegration of $^3$He and $^3$H and the corresponding inverse reactions below $E_γ= 100$ MeV by comparing with our calculations using realistic $NN$ interactions. The theoretical results agree within the errorbars with the data for the total cross sections. Excellent agreement is achieved for the angular distribution in case of $^3$He, whereas for $^3$H a discrepancy between theory and experiment is found.
Three-body photodisintegration of 3He is calculated in the photon energy range 200 - 400 MeV assuming quasifree absorption on np pairs both in initial quasideuteron and singlet configurations. The model includes the normal nucleonic current, explicit meson exchange currents and the Delta(1232)-isobar excitation. The total cross section is increased by a factor of about 1.5 compared with free deuteron photodisintegration. Well below and above the Delta region also some spin observables differ significantly from the ones of free deuteron disintegration due to the more compressed wave function of…
We re-examine the contribution of the $πN$ $S_{31}$ channel to the three-nucleon force for an energy dependent separable potential. Despite the lack of cancellation between the $S_{31}$ and the $P_{11}$ and $P_{33}$ channels, the total contribution of the three-nucleon force to the triton binding is still small.
The relativistic properties of the three-nucleon system are investigated using the Faddeev equations within the Bethe-Salpeter approach. The nucleon-nucleon interaction is chosen in a separable form. The Gauss quadrature method is used to calculate the integrals. The system of the integral equations are solving by iterations method. The binding energy and the partial-wave amplitudes (1S 0 and 3S 1) of the triton are found.
Neutron-deuteron elastic scattering cross sections are calculated at different energies using modern nucleon-nucleon interactions and the Tucson-Melbourne three-nucleon force adjusted to the triton binding energy. Predictions based on NN forces only underestimate nucleon-deuteron data in the minima at higher energies starting around 60 MeV. Adding the three-nucleon forces fills up those minima and reduces the discrepancies significantly.
We consider the correlation between the binding energies of the triton and the alpha-particle which is empirically observed in calculations employing different phenomenological nucleon-nucleon interactions. Using an effective quantum mechanics approach for short-range interactions with large scattering length |a| >> l, where l is the natural low-energy length scale, we construct the effective interaction potential at leading order in l/|a|. In order to renormalize the four-nucleon system, it is sufficient to include a SU(4)-symmetric one-parameter three-nucleon interaction in addition to the S…
Using a generalized Bohr model and the hyper-spherical formalism for a three-body system, we derive the Thomas theorem assuming a simple interaction depending on the range of the potential. We discuss the conditions for which an unbound two-body system produces a bound three-body system and derive universal energy functions. We apply our model to $^{4}$He and Triton atoms as well as to the triton nucleus. Using their scattering lengths and effective ranges, we are able to reproduce the two-body or the three-body binding energies with only one parameter fitted. Prediction for excited (Efimov) l…
We describe systems of two and three nucleons trapped in a harmonic-oscillator potential with interactions from the pionless effective field theory up to next-to-leading order (NLO). We construct the two-nucleon interaction using two-nucleon scattering information. We calculate the trapped levels in the three-nucleon system with isospin $T=1/2$ and determine the three-nucleon force needed for stability of the triton. We extract neutron-deuteron phase shifts, and show that the quartet scattering length is in good agreement with experimental data.
We search for three-neutron resonances which were predicted from pion double charge exchange experiments on He-3. All partial waves up to J=5/2 are nonresonant except the J=3/2^+ one, where we find a state at E=14 MeV energy with 13 MeV width. The parameters of the mirror state in the three-proton system are E=15 MeV and Gamma=14 MeV. The possible existence of an excited state in the triton, which was predicted from a H(He-6,alpha) experiment, is also discussed.
The magnetic form factors of $^2$H, $^3$H, and $^3$He, deuteron photodisintegration cross sections at low energies, and deuteron threshold electrodisintegration cross sections at backward angles in a wide range of momentum transfers, are calculated with the chiral two-nucleon (and three-nucleon) interactions including $Δ$ intermediate states that have recently been constructed in configuration space. The $A\,$=$\,$3 wave functions are obtained from hyperspherical-harmonics solutions of the Schrödinger equation. The electromagnetic current includes one- and two-body terms, the latter induced by…
We calculate higher order corrections for the three-nucleon system up to next-to-next-to-leading within an effective field theory with contact interactions alone. We employ a subtraction formalism previously developed and for which it has been shown that no new three-body force counterterm is needed for complete renormalization up to this order. We give results for the neutron-deuteron phaseshifts and the triton binding energy. Our results are in very good agreement with experimental results and calculations using realistic nucleon-nucleon potentials.
A new framework for computing the Similarity Renormalization Group (SRG) evolution of three-nucleon forces (3NF) in momentum representation is presented. The use of antisymmetric three-particle hyperspherical momentum states ensures unitary evolutions within certain basis truncations, much like antisymmetric harmonic oscillator SRG evolutions. Additionally, in each partial wave the $T_{\mbox{rel}}$-SRG regulator is exactly represented, similar to recent 3NF momentum representation evolutions. Unitary equivalence is demonstrated for the triton using several chiral two- plus three-nucleon intera…
We show how to derive relativistic, unitary, gauge invariant, and charge conserving three-dimensional scattering equations for a system of hadrons interacting with an electromagnetic field. In the method proposed, the spectator equations describing the strong interactions of the hadrons are gauged using our recently introduced gauging of equations method. A key ingredient in our model is the on-mass-shell particle propagator. We discuss how to gauge this on-mass-shell propagator so that both the Ward-Takahashi and Ward identities are satisfied. We then demonstrate our gauging procedure by deri…
We find the threshold structure of the two- and three-nucleon systems, with the deuteron and 3H/3He as the only bound nuclei, sufficient to predict a pair of four-nucleon states: a deeply bound state which is identified with the helium-4 ground state, and a shallow, unstable state at an energy 0.38(25) MeV above the triton-proton threshold which is consistent with data on the first excited state of helium-4. The analysis employs the framework of Pionless EFT at leading order with a generalized regulator prescription which probes renormalization-group invariance of the two states with respect t…
We derive three-body equations valid at finite densities and temperatures. These are based on the cluster mean field approach consistently including proper self energy corrections and the Pauli blocking. As an application we investigate the binding energies of triton and determine the Mott densities and momenta relevant for a many particle description of nuclear matter in a generalized Beth-Uhlenbeck approach. The method, however is not restricted to nuclear physics problems but may also be relevant, e.g., to treat three-particle correlations in weekly doped semiconducters or strongly coupled …
