Diffusion of Ultra High Energy Protons in Galaxy Clusters and Secondary X and Gamma Ray Emissions

In this work we simulate the propagation of Ultra High Energy (UHE) protons in the magnetised intergalactic medium of Galaxy Clusters (GCs). Differently from previous works on the subject, we trace proton trajectories in configurations of the Intra Cluster Magnetic Field (ICMF) which have been extracted from a constrained Magnetic-SPH simulation of the local universe. Such an approach allows us to take into account the effects of several features of the ICMFs, e.g. irregular geometrical structure and field fluctuations due to merger shocks,which cannot be investigated analitically or with usual numerical simulations. Furthermore, we are able to simulate a set of clusters which have properties quite similar to those of GCs observed in the nearby universe. We estimate the time that UHE protons take to get out of the clusters and found that in the energy range 5\times 10^{18} \simleq E \simleq 3 \times 10^{19} \eV proton propagation takes place in the Bohm scattering diffusion regime passing smoothly to a small pitch angle diffusion regime at larger energies. We apply our results to estimate the secondary gamma and Hard X Ray (HXR) emissions produced by UHE protons in a rich GC. We show that the main emission channel is due to the synchrotron HXR radiation of secondary electrons originated by proton photo-pair production scattering onto the CMB. This process may give rise to a detectable signal if a relatively powerful AGN, or a dead quasar, accelerating protons at UHEs is harboured by a rich GC in the local universe.Comment: 27 pages, 13 figure

A Lee-Yang--inspired functional with a density--dependent neutron-neutron scattering length

Inspired by the low--density Lee-Yang expansion for the energy of a dilute Fermi gas of density $\rho$ and momentum $k_F$, we introduce here a Skyrme--type functional that contains only $s$-wave terms and provides, at the mean--field level, (i) a satisfactory equation of state for neutron matter from extremely low densities up to densities close to the equilibrium point, and (ii) a good--quality equation of state for symmetric matter at density scales around the saturation point. This is achieved by using a density--dependent neutron-neutron scattering length $a(\rho$) which satisfies the low--density limit (for Fermi momenta going to zero) and has a density dependence tuned in such a way that the low--density constraint $|a(\rho) k_F| \le 1$ is satisfied at all density scales.Comment: 5 figure

From dilute matter to the equilibrium point in the energy--density--functional theory

Due to the large value of the scattering length in nuclear systems, standard density--functional theories based on effective interactions usually fail to reproduce the nuclear Fermi liquid behavior both at very low densities and close to equilibrium. Guided on one side by the success of the Skyrme density functional and, on the other side, by resummation techniques used in Effective Field Theories for systems with large scattering lengths, a new energy--density functional is proposed. This functional, adjusted on microscopic calculations, reproduces the nuclear equations of state of neutron and symmetric matter at various densities. Furthermore, it provides reasonable saturation properties as well as an appropriate density dependence for the symmetry energy.Comment: 4 figures, 2 table

From bare interactions, low--energy constants and unitary gas to nuclear density functionals without free parameters: application to neutron matter

We further progress along the line of Ref. [Phys. Rev. {\bf A 94}, 043614 (2016)] where a functional for Fermi systems with anomalously large $s$-wave scattering length $a_s$ was proposed that has no free parameters. The functional is designed to correctly reproduce the unitary limit in Fermi gases together with the leading-order contributions in the s- and p-wave channels at low density. The functional is shown to be predictive up to densities $\sim0.01$ fm$^{-3}$ that is much higher densities compared to the Lee-Yang functional, valid for $\rho < 10^{-6}$ fm$^{-3}$. The form of the functional retained in this work is further motivated. It is shown that the new functional corresponds to an expansion of the energy in $(a_s k_F)$ and $(r_e k_F)$ to all orders, where $r_e$ is the effective range and $k_F$ is the Fermi momentum. One conclusion from the present work is that, except in the extremely low--density regime, nuclear systems can be treated perturbatively in $-(a_s k_F)^{-1}$ with respect to the unitary limit. Starting from the functional, we introduce density--dependent scales and show that scales associated to the bare interaction are strongly renormalized by medium effects. As a consequence, some of the scales at play around saturation are dominated by the unitary gas properties and not directly to low-energy constants. For instance, we show that the scale in the s-wave channel around saturation is proportional to the so-called Bertsch parameter $\xi_0$ and becomes independent of $a_s$. We also point out that these scales are of the same order of magnitude than those empirically obtained in the Skyrme energy density functional. We finally propose a slight modification of the functional such that it becomes accurate up to the saturation density $\rho\simeq 0.16$ fm$^{-3}$

Renormalizability of the nuclear many-body problem with the Skyrme interaction beyond mean field

Phenomenological effective interactions like Skyrme forces are currently used in mean--field calculations in nuclear physics. Mean--field models have strong analogies with the first order of the perturbative many--body problem and the currently used effective interactions are adjusted at the mean--field level. In this work, we analyze the renormalizability of the nuclear many--body problem in the case where the effective Skyrme interaction is employed in its standard form and the perturbative problem is solved up to second order. We focus on symmetric nuclear matter and its equation of state, which can be calculated analytically at this order. It is shown that only by applying specific density dependence and constraints to the interaction parameters could renormalizability be guaranteed in principle. This indicates that the standard Skyrme interaction does not in general lead to a renormalizable theory. For achieving renormalizability, other terms should be added to the interaction and employed perturbatively only at first order.Comment: Revised versio

Influence of space allowance on the welfare of weaned buffalo (Bubalus Bubalis) calves

Twenty weaned female buffalo calves were used to evaluate the effect of space allowance in relation to their body surface area on a range of behavioural and physiological parameters. Body surface area in m2 was calculated as 0.12 body weight0.60. Ten calves received 50% of body surface as space allocation (Group 50), 10 others received 90% of body surface area (Group 90). Animals in Group 50 lay with a lower number of outstretched legs than calves in Group 90. Buffaloes from Group 50 were observed standing more frequently than animals from Group 90 ( P < 0.001). The proportions of idling ( P < 0.01) and lying idle observations ( P < 0.001) were higher for Group 90 than for Group 50. Group 90 performed a higher number of non-agonistic interactions than Group 50 ( P < 0.01), whereas the opposite was observed for the number of agonistic interactions ( P < 0.01). When exposed to open field testing, Group 50 animals displayed an increased duration of movement, number of galloping events and more vocalisation. Neither immune responses to phytohemagglutinin and ovalbumin nor the cortisol response to exogenous ACTH were affected by treatment. It was concluded that 50% of body surface area may be an inadequate space allowance for weaned calves

Housing system and welfare of buffalo (Bubalus bubalis) cows

Twenty-eight buffalo cows were used to evaluate the effect of housing system on a range of behavioural and physiological variables. Fourteen cows were group-housed in a loose open-sided barn with a concrete floor and 10 m2 per head as space allowance (group IS). Fourteen others were group-housed in a similar barn but they could also benefit from an outdoor yard with 500 m2 per head as space allowance, free access to potholes for wallowing and spontaneous vegetation (group TS). Animals were subjected to six sessions of instantaneous scan sampling at 10-day intervals. Behavioural variables were expressed as proportions of subjects observed in each category of posture and activity. Phytohaemagglutinin (PHA) was used to perform a skin test based on non-specific delayed type hypersensitivity, whereas 20 mg of ovalbumin were injected subcutaneously to evaluate humoral immune response. Blood samples for evaluation of cortisol concentration were collected immediately prior to exogenous porcine ACTH injection and 1, 2 and 4 h after. The metabolic status of the animals and milk production were also monitored. The proportion of idling animals was higher in group IS than in group TS (P< 0·001). More IS buffalo cows were observed eating at the manger than TS animals (P< 0·001). A higher proportion of TS animals were observed in the sun (P< 0·001). Grazing and bathing activities were recorded only for TS animals. Our findings suggest that buffalo cows kept in intensive conditions and having no access to ample yards and potholes may extend their periods of idling with negative effects on the state of welfare. Immune responses, metabolite concentrations and milk production were not affected by treatment, whereas cortisol levels were higher in IS animals (P< 0·05). The provision of a housing system similar to natural conditions was able to improve the welfare of buffalo cows as indicated by the expression of some species-specific natural behaviours. Such conditions were also associated with lower adrenal cortex response to ACTH injection, possibly as a consequence of the higher degree of initiative allowed to TS cows

Second--order equation of state with the Skyrme interaction. Cutoff and dimensional regularization with the inclusion of rearrangement terms

We evaluate the second--order (beyond--mean--field) contribution to the equation of state of nuclear matter with the effective Skyrme force and use cutoff and dimensional regularizations to treat the ultraviolet divergence produced by the zero--range character of this interaction. An adjustment of the force parameters is then performed in both cases to remove any double counting generated by the explicit computation of beyond--mean--field corrections with the Skyrme force. In addition, we include at second order the rearrangement terms associated to the density--dependent part of the Skyrme force and discuss their effect. Sets of parameters are proposed to define new effective forces which are specially designed for second--order calculations in nuclear matter.Comment: 29 figures, 9 table