The proton-proton fusion reaction, $pp\to de^+ν$, is studied in pionless effective field theory (EFT) with di-baryon fields up to next-to leading order. With the aid of the di-baryon fields, the effective range corrections are naturally resummed up to the infinite order and thus the calculation is greatly simplified. Furthermore, the low-energy constant which appears in the axial-current-di-baryon-di-baryon contact vertex is fixed through the ratio of two- and one-body matrix elements which reproduces the tritium lifetime very precisely. As a result we can perform a parameter free calculation for the process. We compare our numerical result with those from the accurate potential model and previous pionless EFT calculations, and find a good agreement within the accuracy better than 1%.
In this thesis, which is in the field of few-body systems, I am studying low-energy electro-weak interactions in light nuclear systems whose number of nucleons, $A$, is smaller than 4 ({\it i.e.,} $d$, $^3$H, $^3$He), where the main purpose of this work is to calculate the proton-proton ($pp$) fusion rate.
We provide a detailed discussion of the low-energy proton-deuteron system in pionless effective field theory, considering both the spin-quartet and doublet S-wave channels. Extending and amending our previous work on the subject, we calculate the 3He-3H binding energy difference both perturbatively (using properly normalized trinucleon wave functions) and non-perturbatively by resumming all O(alpha) Coulomb diagrams in the doublet channel. Our nonperturbative result agrees well with a calculation that involves the full off-shell Coulomb T-matrix. Carefully examining the cutoff-dependence in th…
We calculate the $β$-decay of tritium at next-to-leading order in pionless effective field theory. At this order, a low-energy parameter $L_{1, A}$ enters the calculation that is also relevant for a high-accuracy prediction of the solar proton-proton fusion rate. We use the tritium half-life to determine this parameter and provide uncertainty estimates. We show proper renormalization of our calculation analyzing the residual cutoff dependence of observables. We find that next-to-leading order corrections contribute about $4\%$ to the triton decay Gamow-Teller strength. We show that these concl…
We calculate the electric dipole moments (EDMs) of three-nucleon systems at leading order in pionless effective field theory. The one-body contributions that arise from permanent proton and neutron EDMs and the two-body contributions that arise from CP-odd nucleon-nucleon interactions are taken into account. Neglecting the Coulomb interaction, we consider the triton and ${}^3$He, and also investigate them in the Wigner-SU(4) symmetric limit. We also calculate the electric dipole form factor and find numerically that the momentum dependence of the electric dipole form factor in the Wigner limit…
This work implements pionless effective field theory with the two-nucleon system expanded around the unitarity limit at second order perturbation theory. The expansion is found to converge well. All Coulomb effects are treated in perturbation theory, including two-photon contributions at next-to-next-to-leading order. After fixing a three-nucleon force to the 3He binding energy at this order, proton-deuteron scattering in the doublet S-wave channel is calculated for moderate center-of-mass momenta.
We consider the two-nucleon weak interaction with a pionless effective field theory. Dibaryon fields are introduced to facilitate calculations and ensure precision in the initial and final state propagators. Weak interactions are accounted for with the parity-violating dibaryon-nucleon-nucleon vertices, which contain unknown weak dibaryon-nucleon-nucleon coupling constants. We apply the model to the calculation of a parity-violating observable in the neutron-proton capture at threshold. Result is obtained up to the linear order in the unknown dibaryon-nucleon-nucleon coupling constants. We com…
We study breakup of the deuteron induced by neutrinos in the neutral $νd\to νnp$, $\barν d\to \barν np$ and the charged $\barν d\to e^+ n n$, $νd\to e^- pp$ processes. Pionless effective field theory with dibaryon fields is used to calculate the total cross sections for neutrino energies $E_ν$ from threshold to 20 MeV. Amplitudes are expanded up to next-to-leading order, and the partial wave is truncated at $P$-waves. The Coulomb interaction between two protons is included nonperturbatively in the reaction amplitudes, and an analytic expression of the amplitudes is obtained. The contribution o…
We calculate low-energy proton--deuteron scattering in the framework of pionless effective field theory. In the quartet channel, we calculate the elastic scattering phase shift up to next-to-next-to-leading order in the power counting. In the doublet channel, we perform a next-to-leading order calculation. We obtain good agreement with the available phase shift analyses down to the scattering threshold. The phase shifts in the region of non-perturbative Coulomb interactions are calculated by using an optimised integration mesh. Moreover, the Coulomb contribution to the 3He-3H binding energy di…
Low energy proton-proton scattering is studied in pionless effective field theory. Employing the dimensional regularization and MS-bar and power divergence subtraction schemes for loop calculation, we calculate the scattering amplitude in 1S0 channel up to next-to-next-to leading order and fix low-energy constants that appear in the amplitude by effective range parameters. We study regularization scheme and scale dependence in separation of Coulomb interaction from the scattering length and effective range for the S-wave proton-proton scattering.
The proton-proton fusion process p p->d e^+ nu_e is calculated at threshold to fifth order in pionless effective field theory. There are two unknown two-body currents contributing at the second and fourth orders. Combined with the previous results for neutrino-deuteron and antineutrino-deuteron scattering, computed to third order in the same approach, we conclude that a 10% measurement of reactor antineutrino-deuteron scattering measurement could constrain the p p->d e^+ nu_e rate to ~7% while a ~3% measurement of nu_e d-> e^- p p could constrain the pp rate to ~2%.
We review our recent calculations of electroweak processes involving the deuteron, based on pionless effective field theory with dibaryon fields. These calculations are concerned with neutron-neutron fusion and np -> d gamma at BBN energies.
The neutron-neutron fusion process, $nn\to deν$, at very low neutron energies is studied in the framework of pionless effective field theory that incorporates dibaryon fields. The cross section and electron energy spectrum for this process are calculated up to next-to-leading order. We include the radiative corrections of ${\cal O}(α)$ calculated for the one-body transition amplitude. The precision of our theoretical estimates is found to be governed essentially by the accuracy with which the empirical values of the neutron-neutron scattering length and effective range are currently known. Als…
The astrophysical S-factor for proton-proton fusion, S_11(E), is obtained with the nuclear matrix element analytically calculated in pionless effective field theory. To the third order, the zero-energy result S_11(0) and the first energy derivative S'_11(0) are found to be (3.99 \pm 0.14)* 10^-25 MeV b and S_11(0)*(11.3 \pm 0.1) MeV^-1, respectively; both consistent with the current adopted values. The second energy derivative is also calculated for the first time, and the result S"_11(0) = S_11(0)*(170 \pm 2) MeV^-2 contributes at the level of 0.5% to the fusion rate at the solar center, whic…
We present a new perturbative expansion for pionless effective field theory with Coulomb interactions in which at leading order the spin-singlet nucleon-nucleon channels are taken in the unitarity limit. Presenting results up to next-to-leading order for the Phillips line and the neutron-deuteron doublet-channel phase shift, we find that a perturbative expansion in the inverse 1S0 scattering lengths converges rapidly. Using a new systematic treatment of the proton-proton sector that isolates the divergence due to one-photon exchange, we renormalize the corresponding contribution to the 3H-3He …
Proton-proton fusion is considered in the effective field theory of Kaplan, Savage and Wise. Coulomb effects are included systematically in a non-perturbative way. Including the dimension-eight derivative coupling which determines the effective ranges of the scattering amplitudes, next-to-leading order corrections to the fusion rate are calculated. When the renormalization mass is well above the characteristic energies of the system, this contribution gives a rate which is eight percent below the standard value. The difference can be due to an unknown counterterm which comes in at this order.
The total cross section for radiative neutron capture on a proton, $np \to d γ$, is evaluated at big bang nucleosynthesis (BBN) energies. The electromagnetic transition amplitudes are calculated up to next-to leading order within the framework of pionless effective field theory with dibaryon fields. We also calculate the $dγ\to np$ cross section and the photon analyzing power for the $d\vecγ\to np$ process from the amplitudes. The values of low energy constants that appear in the amplitudes are estimated by a Markov Chain Monte Carlo analysis using the relevant low energy experimental data. Ou…
We calculate the $p$-wave contribution to the proton-proton fusion $S$ factor and its energy derivative in pionless effective field theory (EFT) up to next-to-leading order. The leading contributions are given by a recoil piece from the Gamow-Teller and Fermi operators, and from relativistic $1/m$ suppressed weak interaction operators. We obtain the value of $(2.5\pm0.3 )\times 10^{-28}~\mathrm{MeV\ fm^2}$ for the $S$ factor and $(2.2\pm0.2) \times 10^{-26}~\mathrm{fm^2}$ for its energy derivative at threshold. These are smaller than the results of a prior study that employed chiral EFT by sev…
The proton-proton ($pp$) fusion cross-section found at the heart of solar models is unconstrained experimentally and relies solely on theoretical calculations. Effective field theory provides an opportunity to constrain the $pp$ cross-section experimentally, however, this method is complicated by the appearance of two-nucleon effects in the form of an unknown parameter $L_{1,A}$. We present a method to constrain $L_{1,A}$ using the Standard Solar Model and helioseismology. Using this method, we determine a value of $L_{1,A}$ = 7.0 fm$^{3}$ with a range of 1.6 to 12.4 fm$^{3}$. These results ar…
We test the Salpeter formalism for the electron screening of the solar proton-proton fusion reaction by solving numerically the relevant Schrodinger equation. We evaluate exactly the square of the overlap integral of the two-proton wave function and the deuteron wave function and compare with the usual analytic approximation. The usual WKB solution agrees with the numerical result to $O(10^{-4})$. The WKB approximation should be even more precise for the other nuclear fusion reactions in the $pp$ chain and CNO cycles.
Spurred by the recent complete determination of the weak currents in two-nucleon systems up to ${\cal O}(Q^3)$ in heavy-baryon chiral perturbation theory, we carry out a parameter-free calculation of the solar proton fusion rate in an effective field theory that combines the merits of the standard nuclear physics method and systematic chiral expansion. Using the tritium beta-decay rate as an input to fix the only unknown parameter in the effective Lagrangian, we can evaluate with drastically improved precision the ratio of the two-body contribution to the well established one-body contribution…
The rate for the fusion process $p + p \ra d + e^+ + ν_e$ is calculated using non-relativistic effective field theory. Including the four-nucleon derivative interaction, results are obtained in next-to-leading order in the momentum expansion. This reproduces the effects of the effective range parameter. Coulomb interactions between the incoming protons are included non-perturbatively in a systematic way. The resulting fusion rate is independent of specific models and wavefunctions for the interacting nucleons. At this order in the effective Lagrangian there is an unknown counterterm which limi…
Renormalization of proton-proton fusion is studied in the framework of chiral effective field theory. Strict perturbative treatment of subleading corrections is applied in the analysis. Possible enhancement of two-nucleon contact axial current operators is the focus of the study. We find evidence that supports a previous proposal in the literature to promote one of the contact axial current operators.
Spurred by the recent complete determination of the weak currents in two-nucleon systems up to ${\cal O}(Q^3)$ in heavy-baryon chiral perturbation theory, we carry out a parameter-free calculation of the threshold $S$-factors for the solar $pp$ (proton-fusion) and $hep$ processes in an effective field theory that {\it combines} the merits of the standard nuclear physics method and systematic chiral expansion. The power of the EFT adopted here is that one can correlate in a unified formalism the weak-current matrix elements of two-, three- and four-nucleon systems. Using the tritium $β$-decay r…
Using a recently developed effective field theory for the interactions of nucleons at non-relativistic energies, we calculate the rate for the fusion process $p + p \ra d + e^+ + ν_e$ to leading order in the momentum expansion. Coulomb effects are included non-perturbatively in a systematic way. The resulting rate is independent of specific models for the strong interactions at short distances and is in agreement with the standard result in the zero-range approximation.
The spectrum of a system with multiple channels composed of two hadrons with nonzero total momentum is determined in a finite cubic volume with periodic boundary conditions using effective field theory methods. The results presented are accurate up to exponentially suppressed corrections in the volume due to the finite range of hadronic interactions. The formalism allows one to determine the phase shifts and mixing parameters of pipi-KK isosinglet coupled channels directly from Lattice Quantum Chromodynamics. We show that the extension to more than two channels is straightforward and present t…
The proton-proton fusion rate is calculated at low energy in a lattice effective field theory (EFT) formulation. The strong and the Coulomb interactions are treated non-perturbatively at leading order in the EFT. The lattice results are shown to accurately describe the low energy cross section within the validity of the theory at energies relevant to solar physics. In prior work in the literature, Coulomb effects were generally not included in non-perturbative lattice calculations. Work presented here is of general interest in nuclear lattice EFT calculations that involve Coulomb effects at lo…
The study of long-range correlations between observables in two rapidity windows was proposed as a signature of the string fusion and percolation phenomenon. In the present work we calculate the correlation functions and coefficients for p-Pb collisions in the framework of the Monte Carlo string-parton model, based on the picture of elementary collisions of color dipoles. It describes pA and AA scattering without referring to the Glauber picture of independent nucleons collisions and includes effects of string fusion. Different types of correlations are considered: n-n, pt-n, pt-pt, where n is…
To explain the experimental facts that the fusion cross sections of proton-halo nucleus on heavy target nucleus is not enhanced as expected, the shielding supposition has been proposed. Namely, the proton-halo nucleus is polarized with the valence proton being shielded by the core. In this paper, within the frame of the Improved Quantum Molecular Dynamics model, the fusion reactions by $^{17}$F on $^{208}$Pb around Coulomb barrier have been simulated. The existence of shielding effect is verified by microscopic dynamics analysis and its influence on the effective interaction potential is also …
Bayesian analysis of proton-proton fusion in chiral effective field theory
Johannes Gutenberg Universität Mainz（约翰内斯·古腾堡美因茨大学）；Università di Pisa（比萨大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Pisa（意大利国家核物理研究所，比萨分部）；Old Dominion University（老道明大学）；Jefferson Lab（杰斐逊实验室）
In this short note we use a simple model to describe the dynamical effects of break-up processes in the subbarrier fusion involving weakly bound nuclei. We model two similar cases involving either a neutron or a proton halo nucleus, both schematically coupled to the break-up channels. We find that the decrease of the coulomb barrier in the proton break-up channel leads, ceteris paribus, to a larger enhancement of the subbarier fusion probabilities with respect to the neutron-halo case.
We investigate the proton-boron nuclear fusion cross sections under the influence of the intense linearly polarized monochromatic laser fields with high frequency. First, we rewrite the time-dependent Schrödinger equation using Kramers-Henneberger (KH) transformation which allows for shifting all time dependence of the problem into the potential function. Then, for the intense laser fields that satisfy the high frequency limit, the time-averaged scheme in the KH framework should be valid. We can use WKB approximation to evaluate Coulomb barrier penetrability and then calculate proton-boron nuc…
The nuclear matrix element determining the $pp\to d e^+ ν$ fusion cross section and the Gamow-Teller matrix element contributing to tritium $β$-decay are calculated with lattice Quantum Chromodynamics (QCD) for the first time. Using a new implementation of the background field method, these quantities are calculated at the SU(3)-flavor-symmetric value of the quark masses, corresponding to a pion mass of $m_π$ ~ 806 MeV. The Gamow-Teller matrix element in tritium is found to be 0.979(03)(10) at these quark masses, which is within $2σ$ of the experimental value. Assuming that the short-distance …
We study theoretically fusion of the light proton-rich exotic nuclei $^{17}$F and $^8$B at near-barrier energies in order to investigate the possible role of breakup processes on their fusion cross sections. To this end, coupled channel calculations are performed considering the couplings to the breakup channels of these projectiles. In case of $^{17}$F, the coupling arising out of the inelastic excitation from the ground state to the bound excited state and its couplings to the continuum have also been taken into consideration. It is found that the inelastic excitation/breakup of $^{17}$F aff…
The velocity dependence of the stopping power of swift protons and deuterons in low energy collisions is investigated. At low projectile energies the stopping is mainly due to nuclear stopping and charge exchange of the electron. The second mechanism dominates after Ep >=200 eV. A dynamical treatment of the charge exchange mechanism based on two-center electronic wavefunctions yields very transparent results for the exchange probability. We predict that the stopping cross sections vary approximately as v to the 1.35 power for projectile protons on hydrogen targets in the 1 keV energy region.
An analysis of the astrophysical $S$ factor of the proton-proton weak capture ($\mathrm{p}+\mathrm{p}\rightarrow {}^2\mathrm{H}+\mathrm{e}^++ν_{\mathrm{e}}$) is performed on a large energy range covering solar-core and early Universe temperatures. The measurement of $S$ being physically unachievable, its value relies on the theoretical calculation of the matrix element $Λ$. Surprisingly, $Λ$ reaches a maximum near $0.13~\mathrm{MeV}$ that has been unexplained until now. A model-independent parametrization of $Λ$ valid up to about $5~\mathrm{MeV}$ is established on the basis of recent effective…
We present a power counting to include Coulomb effects in the three-nucleon system in a low-energy pionless effective field theory (EFT). With this power counting, the quartet S-wave proton-deuteron elastic scattering amplitude is calculated. The calculation includes next-to-leading order (NLO) Coulomb effects and next-to-next-to-leading order (NNLO) strong interaction effects, with an estimated theoretical error of about 7 %. The EFT results agree with potential model calculations and phase shift analysis of experimental data within the estimated errors.
Experimental above-barrier fusion cross-sections for $^{17}$F + $^{12}$C are compared to the fusion excitation functions for $^{16,18}$O, $^{19}$F, and $^{20}$Ne ions on a carbon target. In comparing the different systems both the differing static size of the incident ions and changes in fusion barrier are accounted for by examining the reduced fusion cross-section. Remaining trends of the fusion cross-section above the barrier which reflect the sensitive interplay of the sd protons and neutrons are observed. The experimental data are also compared to both a widely-used analytical model of nea…
The nuclear reaction e+p+d -----> He3 + e is considered at thermonuclear energies. The motion of the electron is treated within the adiabatic approximation and the pd scattering state is constructed in the form of an antisymmetrized product of the bound state wave function of the deuteron and of the wave function of the pd relative motion. The latter is calculated using an effective pd potential constructed via the Marchenko inverse scattering method. The bound state wave function of He3 is obtained using Faddeev--type integrodifferential equations. The reaction rate thus obtained for the sola…
We discuss the possibility of the non-one-neutron emission channels in the cold fusion reaction $^{70}$Zn + $^{209}$Bi to produce the element Z=113. For this purpose, we calculate the evaporation-residue cross sections of one-proton, radiative-capture, and two-neutron emissions relative to the one-neutron emission in the reaction $^{70}$Zn + $^{209}$Bi. To estimate the upper bounds of those quantities, we vary model parameters in the calculations, such as the level-density parameter and the height of the fission barrier. We conclude that the highest possibility is for the 2n reaction channel, …
Studies of the ultrarelativistic collisions of hadrons and nuclei at different centrality and energy enable to explore the QCD phase diagram in a wide range of temperature and baryon density. Long-range correlation studies are considered as a tool, sensitive to the observation of phase transition and the critical point. In the present work, a Monte Carlo model of proton-proton, proton-nucleus, and nucleus-nucleus collisions is applied to heavy and light ion collisions at the cms energy range from a few up to several hundred GeV per nucleon. The model describes the nuclear collisions at the par…
Systematic examination of fusion for $^{39,41,45,47}$K + $^{28}$Si and $^{36,44}$Ar + $^{28}$Si provides insight into the impact of neutron and proton exchange on fusion for nuclei at and near the N=20 and N=28 shells. Comparison of the reduced excitation functions reveals a marked difference between the behavior of open-shell and closed-shell systems. While coupled channels calculations provide a good description for the closed-shell nuclei they significantly under-predict the fusion cross-section for open-shell nuclei. The observed trends are examined in the context of a potential energy sur…
Within the framework of the dinuclear system model, production cross sections of proton-rich nuclei with charged numbers of Z=84-90 are investigated systematically. Possible combinations with the $^{28}$Si, $^{32}$S, $^{40}$Ar bombarding the target nuclides $^{165}$Ho, $^{169}$Tm, $^{170-174}$Yb, $^{175,176}$Lu, $^{174,176-180}$Hf and $^{181}$Ta are analyzed thoroughly. The optimal excitation energies and evaporation channels are proposed to produce the proton-rich nuclei. The systems are feasible to be constructed in experiments. It is found that the neutron shell closure of N=126 is of impor…
The behaviors of barrier characteristics and fusion cross sections are analyzed by changing neutron over wide range of colliding systems. For this purpose, we have extended our previous study (Eur. Phys. J. A \textbf{48}, 21 (2012), it is devoted to the colliding systems with neutron-rich nuclei) to 125 isotopic systems with condition of $0.5\leq N/Z \leq 1.6$ for their compound nuclei. The AW 95, Bass 80, Denisov DP and Prox. 2010 potentials are used to calculate the nuclear part of interacting potential. The obtained results show that the trend of barrier heights $V_B$ and positions $R_B$ as…
The relativistic field theory model of the deuteron is applied to the calculation of the cross sections of the low-energy radiative neutron-proton capture n + p -> D + gamma and the low-energy two-proton fusion p + p -> D + e^+ + nu_e. For the low-energy radiative neutron-proton capture n + p -> D + gamma our result agrees well with both the experimental data and the potential model prediction. In the case of the two-proton fusion the cross section obtained is 2.9 times as much as that given by the potential approach. The obtained result is discussed in connection with the solar neutrino probl…
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…
In a fusion reactor, a proton and a neutron generated in previous reactions may again fuse with each other. Or they can in turn fuse with or be captured by an un-reacted deuteron. The average center-of-mass (COM) energy for such reaction is around 10 keV in a typical fusion reactor, but could be as low as 1 keV. At this low COM energy, the reacting nucleons are in an s-wave state in terms of their relative angular momentum. The single-gamma radiation process is thus strongly suppressed due to conservation laws. Instead the gamma ray released is likely to be accompanied by x-ray photons from a …
We compute the $S$-factor of the proton-proton ($pp$) fusion reaction using chiral effective field theory ($χ$EFT) up to next-to-next-to-leading order (NNLO) and perform a rigorous uncertainty analysis of the results. We quantify the uncertainties due to (i) the computational method used to compute the $pp$ cross section in momentum space, (ii) the statistical uncertainties in the low-energy coupling constants of $χ$EFT, (iii) the systematic uncertainty due to the $χ$EFT cutoff, and (iv) systematic variations in the database used to calibrate the nucleon-nucleon interaction. We also examine th…
Temperature and kinematic line broadening are the primary contributions to the width of the proton energy spectrum measured in cluster-impact fusion experiments. By ascertaining these two contributions, we have determined an effective temperature for the high-velocity deuteron component that is responsible for the measured fusion yield. The extracted effective temperature is substantially higher than conventional estimates., and implies that cluster-impact fusion is hot fusion on an atomic scale. The proton spectrum rules out contaminants in explaining the high yield.
