How does a positron differ from an electron

The electron and positron capture rates are calculated over a wide temperature 0. Weak interactions and gravity decide the fate of a star. These two processes play a vital role in the evolution of stars. Weak interactions deleptonize the core of massive star, determine the final electron fraction Y e , and the size of the homologous core. The collapse is very sensitive to the entropy and to the number of leptons per baryons, Y e , [1]. Electron capture and photodisintegration processes in the stellar interior cost the core energy by reducing the electron density and as a result the collapse of stellar core is accelerated under its own ferocious gravity.

This collapse of the stellar core is very sensitive to the core entropy and to the number of lepton to baryon ratio. These two quantities are mainly determined by weak interaction processes. The simulation of the core collapse is very much dependent on the electron capture on heavy nuclides [2].

When the stellar core attains densities close to 10 9 gcm -3 , it consists of heavy nuclei imbued in electrically neutral plasma of electrons, with small fraction of drip neutrons and an even smaller fraction of drip protons [3].

At this stage the density of the stellar core is much lower than the nuclear matter density and thus the average volume available to a single nucleus is much greater than that of nuclear volume. Electron capture and beta decay decide the ultimate fate of the star. During the stellar core collapse, the entropy of the stellar core decides whether the electron capture occur on heavy nuclei or on free protons produced in the photodisintegration process.

Electron capture on nuclei takes place in very dense environment of the stellar core where the Fermi energy chemical potential of the degenerate electron gas is sufficiently large to overcome the threshold energy given by negative Q values of the reactions involved in the interior of the stars.

This high Fermi energy of the degenerate electron gas leads to enormous electron capture on nuclei and results in the reduction of the electron to baryon ratio Y e. In the late stage of the star evolution, energies of the electrons are high enough to induce transitions to the GT resonance. The importance of electron capture for the presupernova collapse is also discussed in Ref.

The positron captures are of key importance in stellar core, especially in high temperatures and low density locations. The competition and perhaps equilibrium between positron captures on neutrons and electron captures on protons is an important ingredient of the modeling of Type-II supernovae.

Recognizing the pivotal role played by capture process, Fuller et al. They stressed on the importance of capture process to the GT resonance. The FFN rates were then updated taking into account quenching of GT strength by an overall factor of two by Aufderheide et al.

The authors stressed the need of a microscopic theory for calculation of reliable rates vital for simulation codes of core collapse. Two fully microscopic approaches, i. In shell model emphasis is more on interactions as compared to correlations whereas QRPA puts more weight in correlations. Shell model calculations are normally done taking a big core and some few nucleons in the valence orbital.

The QRPA calculations on the other hand take all nucleons in the valence orbital and approximately none in the core. Because of the large dimensionality of the space involved for the pf-shell nuclei and beyond, Hamiltonian diagonalization and calculation of beta decay strength is computationally a formidable task. These calculations, unfortunately, do not allow for detailed spectroscopy. Secondly, the Monte Carlo path integral techniques are limited to interactions that are free of the the "sign problem" and are still computationally very intensive i.

The QRPA approach gives us the liberty of performing calculations in a luxurious model space as big as 7 w. Langanke and collaborators [10] pointed out that QRPA is the method of choice for dealing with heavy nuclei, and for predicting their half-lives, in particular, based on the calculation of the GT strength function.

The QRPA method considers the residual correlations among nucleons via one particle one hole 1p-1h excitations in a large multi- w model spaces. An important extension of the model in Ref. Halbleib and Sorensen [12] for the first time proposed and applied the pn-QRPA theory with separable GT or Fermi interactions on spherical harmonic basis and later it was extended to deformed nuclei [13, 14] using deformed single particle basis.

This work is based on the pn-QRPA theory. We performed the evaluation of the weak interaction rates and summed them over all parent and daughter states to get the total rate. We considered a total of 30 excited states in parent nucleus. The inclusion of a very large model space of 7 w in our model provides enough space to handle excited states in parent and daughter nuclei around which leads to satisfactory convergence of the electron capture rates see Eq. Transitions between these states play an important role in the calculated weak rates.

All previous compilations of weak interaction rates either ignore transitions from parent excited states due to complexity of the problem or apply the so-called Brink's hypothesis when taking these excited states into consideration. This hypothesis assumes that the Gamow-Teller strength distribution on the excited states is same as for the ground state, only shifted by the excitation energy of the state.

We do not use Brink's hypothesis to estimate the Gamow-Teller transitions from parent excited states but rather we performed a state-by-state evaluation of the weak interaction rates and summed them over all parent and daughter sates to get the total weak rate. This is the second major difference between this work and previous calculations of electron capture rates.

The result is an enhancement of electron capture rates on 55 Co compared to the earlier reported rates. Reliability of calculated rates is a key issue and of decisive importance for many simulation codes.

The reliability of pn-QRPA model has already been established and discussed in detail [11, 15, 16, 17]. There the authors compared the measured data of thousands of nuclides with the pn-QRPA calculations and got good comparison. Heger and collaborators [18] identified 55 Co as the most important nuclide for electron capture for massive stars Here we also compare our results with the previous compilations.

The formalism used to calculate weak rates at high temperatures and densities relevant to stellar environment using the pn-QRPA theory is discussed in this section. The following assumptions are made in the calculation of weak rates. It is assumed that contributions from forbidden transitions are relatively negligible. The electrons are not bound anymore to the nucleus and obey the Fermi-Dirac distribution. Therefore, there are no anti neutrinos which block the emission of these particles in the capture or decay processes.

Also, anti neutrino capture is not taken into account. Here H sp is the single-particle Hamiltonian, V pair is the pairing force, is the particle-hole ph Gamow-Teller force, and is the particle particle pp Gamow-Teller force.

Wave functions and single particle energies are calculated in the Nilsson model [20], which takes into account the nuclear deformations. Pairing is treated in the BCS approximation. Positron binding energies have been measured for a large variety of small targets [1] , although only a few calculations are available [1].

Positron scattering in the gases phase constitutes a sensitive test for atomic interactions. The static potential between the incoming electron and the fixed charge distribution in an atom is attractive. Positrons inside an atom experience a repulsive static interaction from the positive nucleus only partially screened by electrons.

New scattering measurements are very important for comparison, setting new standards for both theoreticians and experimentalists [1,2]. Indeed one rationale for the present investigation is to try and shed more light on this state of affairs.

In the last few years, there have been several theoretical activities concerning the positron-atom scattering at several energies [3]. Most of the work produced was based on ab initio methods [3] and also classical collision theory [3]. However, each of these models works only on a limited range of targets and these calculations are very time consuming, limiting the domain of applicability of such models. In the present work we present a study on the simple scaling of plane wave Born cross section which was created for positron-impact excitations of targets in general [4].

The study is based on the traditional first Born approximation FBA. The FBA still is used as the starting point in several studies, because a the plane wave is the correct wave function at infinity for an positron colliding with a target, and b it is the simplest collision theory that uses target wave function explicitly.

Validating a scaling method for FBA cross sections of atoms requires two initial ingredients: i the Born integral cross sections themselves; ii reliable experimental or theoretical optical oscillator strengths.

The called BE f -scaling approach was found by Kim [5] to convert the FBA to reliable cross sections comparable to accurate excitation cross sections at all incident electron energies above threshold. The BE f -scaling described by Kim [5] correct the deficiencies of FBA into simple functional forms that depend on a few atomic properties.

Cross sections for positron and electron impact are virtually identical at high energies and if the basic dynamical ingredients for this evidence is the FBA, then it is possible extend the analysis developed by Kim [5] to more complicated systems, as positron-atom scattering this is a important consideration and can be significant for studies using positron as incident particle [4].

One of the complications created by the use of positron as incident particle is the existence of additional positronium channels which are not present in the case of electron scattering. Thus, we will present a study of the SBP approach without Ps channel. The goal of the present scaling method is to provide a simple theoretical method to calculate excitation cross sections comparable not only to reliable experimental data, but also to more sophisticated theories. To our knowledge, this study represents the first attempt to establish a theoretical formulation for positron scattering using the called scaling Born positron SBP , i.

In Sec. Conclusions are presented in Sec. The scaling Born approximation described by Kim [5] for excitation of neutral atoms is applicable to dipole-allowed excitations, and use atomic properties as excitation energy, ionization energy, and the dipole f value that can be obtained, in principle, from accurate wave functions.

Since scaled cross sections are based on the plane wave Born approximation FBA , they do not account for the resonances often found near the excitation thresholds. We will see that our method for positron scattering not only reduces the cross sections magnitude at low energy, but also shifts the peak to a high energy than the peak of the unscaled FBA, while keeping the high energy validity of the Born approximation intact.

The SBP cross sections are described as. The amplitude for the FBA is given by. In Eq. Scattering amplitude obtained from FBA are valid for high-energy static calculations, i. When they meet, the positron and the electron, which are Antiparticles of each other, destroy themselves mutually, they annihilate.

Two annihilation gamma with equal energy are also emitted back to back. They carry each keV, that is the mass energy of the two particles which is thus restored. This characteristic annhihilation reaction is used in nuclear medicine for the screening of cancers.

Moving in the midst of its countless electron enemies, positrons are virtually absent from our environment. The same happens to antiprotons.

How to explain this lack of antimatter around us, while at the elementary level whenever a particle is created or destroyed, an antiparticle is created or destroyed too.

Where is the antimatter? This is one of the major questions addressed particle physics. Experiments have shown that a perfect symmetry between particles and antiparticles is not perfectly respected in the field of the weak forces responsibles in particular of beta radioactivity. Can this asymmetry ,which is vety small, be the explanation of antimatter absence around us? Access to page in french. It causes the reduction of the atomic number. However, the mass number of the atom will remain the same.

This is because the proton is converted into a neutron and the mass number is the sum of protons and neutrons in the atom. Following nuclear reaction is an example of positron emission. This is an isotope of carbon.

It is a radioactive isotope of carbon. It decays to boron via positron emission. Boron is a stable isotope of boron. Electron capture is a type of radioactive decay where the nucleus of an atom absorbs an inner shell electron and converts a proton into a neutron releasing an electron neutrino and gamma radiation.

This process takes place in proton-rich nuclei. An inner shell electron is an electron from an inner energy level of the atom ex: K shell, L shell.

Simultaneously, this process causes the release of an electron neutrino. The nuclear reaction for the process can be given as follows.