We provide a brief commentary on recent work by Hammer and Son on the scaling behavior of nuclear reactions involving the emission of several loosely bound neutrons. In this work they discover a regime, termed unnuclear physics, in which these reacti
ons are governed by an approximate conformal symmetry of the nuclear force. Remarkably, the scaling exponents that govern nuclear reactions can be related to the energies of ultracold atomic drops confined in harmonic potentials. We also comment on the importance and the limitations of this approximate symmetry in the physics of neutron stars.
We consider the scattering of dark matter particles from superfluid liquid $^4$He, which has been proposed as a target for their direct detection. Focusing on dark matter masses below ~1 MeV, we demonstrate from sum-rule arguments the importance of t
he production of single phonons with energies $omega lesssim 1$ meV. We show further that the anomalous dispersion of phonons in liquid $^4$He at low pressures [i.e., $d^2omega(q)/dq^2>0$, where $q$ and $omega(q)$ are the phonon momentum and energy] has the important consequence that a single phonon will decay over a relatively short distance into a shower of lower energy phonons centered on the direction of the original phonon. Thus the experimental challenge in this regime is to detect a shower of low energy phonons, not just a single phonon. Additional information from the distribution of phonons in such a shower could enhance the determination of the dark matter mass.
Stirling Colgate was a remarkably imaginative physicist, an independent thinker with a wide breadth of interests and contagious enthusiasm, a born leader with enduring drive to attack fundamental problems in science. Among his many achievements, he f
ounded the quantitative theory of stellar collapse and supernova explosions, and introduced numerical simulation into the astrophysical toolbox. He brought strong physical intuition to both theory and experiment, in the sciences of nuclear weapons, magnetic and inertial fusion, as well as astrophysics.
We demonstrate that the observation of neutron stars with masses greater than one solar mass places severe demands on any exotic neutron decay mode that could explain the discrepancy between beam and bottle measurements of the neutron lifetime. If th
e neutron can decay to a stable, feebly-interacting dark fermion, the maximum possible mass of a neutron star is 0.7 solar masses, while all well-measured neutron star masses exceed one solar mass. The survival of $2 M_odot$ neutron stars therefore indicates that any explanation beyond the Standard Model for the neutron lifetime puzzle requires dark matter to be part of a multi-particle dark sector with highly constrained interactions.
The neutron, in addition to possibly having a permanent electric dipole moment as a consequence of violation of time-reversal invariance, develops an induced electric dipole moment in the presence of an external electric field. We present here a unif
ied non-relativistic description of these two phenomena, in which the dipole moment operator, $vec{cal D}$, is not constrained to lie along the spin operator. Although the expectation value of $vec{cal D}$ in the neutron is less than $10^{-13}$ of the neutron radius, $r_n$, the expectation value of $vec {cal D},^2$ is of order $r_n^2$. We determine the spin motion in external electric and magnetic fields, as employed in past and future searches for a permanent dipole moment, and show that the neutron electric polarizability, although entering the neutron energy in an external electric field, does not affect the spin motion. In a simple non-relativistic model we show that the expectation value of the permanent dipole is, to lowest order, proportional to the product of the time reversal-violating coupling strength and the electric polarizability of the neutron.
We calculate the effect of a heat current on transporting $^3$He dissolved in superfluid $^4$He at ultralow concentration, as will be utilized in a proposed experimental search for the electric dipole moment of the neutron (nEDM). In this experiment,
a phonon wind will generated to drive (partly depolarized) $^3$He down a long pipe. In the regime of $^3$He concentrations $tilde < 10^{-9}$ and temperatures $sim 0.5$ K, the phonons comprising the heat current are kept in a flowing local equilibrium by small angle phonon-phonon scattering, while they transfer momentum to the walls via the $^4$He first viscosity. On the other hand, the phonon wind drives the $^3$He out of local equilibrium via phonon-$^3$He scattering. For temperatures below $0.5$ K, both the phonon and $^3$He mean free paths can reach the centimeter scale, and we calculate the effects on the transport coefficients. We derive the relevant transport coefficients, the phonon thermal conductivity and the $^3$He diffusion constants from the Boltzmann equation. We calculate the effect of scattering from the walls of the pipe and show that it may be characterized by the average distance from points inside the pipe to the walls. The temporal evolution of the spatial distribution of the $^3$He atoms is determined by the time dependent $^3$He diffusion equation, which describes the competition between advection by the phonon wind and $^3$He diffusion. As a consequence of the thermal diffusivity being small compared with the $^3$He diffusivity, the scale height of the final $^3$He distribution is much smaller than that of the temperature gradient. We present exact solutions of the time dependent temperature and $^3$He distributions in terms of a complete set of normal modes.
Motivated by a proposed experimental search for the electric dipole moment of the neutron (nEDM) utilizing neutron-$^3$He capture in a dilute solution of $^3$He in superfluid $^4 $He, we derive the transport properties of dilute solutions in the regi
me where the $^3$He are classically distributed and rapid $^3$He-$^3$He scatterings keep the $^3$He in equilibrium. Our microscopic framework takes into account phonon-phonon, phonon-$^3$He, and $^3$He-$^3$He scatterings. We then apply these calculations to measurements by Rosenbaum et al. [J.Low Temp.Phys. {bf 16}, 131 (1974)] and by Lamoreaux et al. [Europhys.Lett. {bf 58}, 718 (2002)] of dilute solutions in the presence of a heat flow. We find satisfactory agreement of theory with the data, serving to confirm our understanding of the microscopics of the helium in the future nEDM experiment.
We review the history of neutron star physics in the 1930s that is related to L. Landau. According to recollections of Rosenfeld (1974, Proc. 16th Solvay Conference on Physics, p. 174), Landau improvised the concept of neutron stars in a discussion w
ith Bohr and Rosenfeld just after the news of the discovery of the neutron reached Copenhagen in February 1932. We present arguments that the discussion took place in March 1931, before the discovery of the neutron, and that they in fact discussed the paper written by Landau in Zurich in February 1931 but not published until February 1932 (Phys. Z. Sowjetunion, 1, 285). In his paper Landau mentioned the possible existence of dense stars which look like one giant nucleus; this can be regarded as an early theoretical prediction or anticipation of neutron stars, prior to the discovery of the neutron. The coincidence of the dates of the neutrons discovery and the papers publication has led to an erroneous association of the paper with the discovery of the neutron. In passing, we outline the contribution of Landau to the theory of white dwarfs and to the hypothesis of stars with neutron cores.
Using arguments based on sum rules, we derive a general result for the average shifts of rf lines in Fermi gases in terms of interatomic interaction strengths and two-particle correlation functions. We show that near an interaction resonance shifts v
ary inversely with the atomic scattering length, rather than linearly as in dilute gases, thus accounting for the experimental observation that clock shifts remain finite at Feshbach resonances.
We examine the phase diagram of a Bose-Einstein condensate of atoms, interacting with an attractive pseudopotential, in a quadratic-plus-quartic potential trap rotating at a given rate. Investigating the behavior of the gas as a function of interacti
on strength and rotational frequency of the trap, we find that the phase diagram has three distinct phases, one with vortex excitation, one with center of mass excitation, and an unstable phase in which the gas collapses.
