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تسجيل مستخدم جديدHow to increase the applicability of integral transform approaches in physics?
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Integral transform approaches are numerous in many fields of physics, but in most cases limited to the use of the Laplace kernel. However, it is well known that the inversion of the Laplace transform is very problematic, so that the function related to the physical observable is in most cases unaccessible. The great advantage of kernels of bell-shaped form has been demonstrated in few-body nuclear systems. In fact the use of the Lorentz kernel has allowed to overcome the stumbling block of the ab initio description of reactions to the full continuum of systems of more than three particles. The problem of finding kernels of similar form, applicable to many-body problems deserves particular attention. If this search were successful the integral transform approach might represent the only viable ab initio access to many observables that are not calculable directly.
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The LIT approach is reviewed both for inclusive and exclusive reactions. It is shown that the method reduces a continuum state problem to a bound-state-like problem, which then can be solved with typical bound-state techniques. The LIT approach opens
up the possibility to perform ab initio calculations of reactions also for those particle systems which presently are out of reach in conventional approaches with explicit calculations of many-body continuum wave functions. Various LIT applications are discussed ranging from particle systems with two nucleons up to particle systems with seven nucleons.
The Lorentz integral transform method is briefly reviewed. The issue of the inversion of the transform, and in particular its ill-posedness, is addressed. It is pointed out that the mathematical term ill-posed is misleading and merely due to a histor
ical misconception. In this connection standard regularization procedures for the solution of the integral transform problem are presented. In particular a recent one is considered in detail and critical comments on it are provided. In addition a general remark concerning the concept of the Lorentz integral transform as a method with a controlled resolution is made.
A brief outline of the Lorentz Integral Transform (LIT) method is given. The method is well established and allows to treat reactions into the many-body continuum with bound-state like techniques. The energy resolution that can be achieved is studied
by means of a simple two-body reaction. From the discussion it will become clear that the LIT method is an approach with a controlled resolution and that there is no principle problem to even resolve narrow resonances in the many-body continuum. As an example the isoscalar monopole resonance of 4He is considered. The importance of the choice of a proper basis for the expansion of the LIT states is pointed out. Employing such a basis a width of 180(70) keV is found for the 4He isoscalar monopole resonance when using a simple central nucleon-nucleon potential model.
The application of the Lorentz integral transform (LIT) method to photon scattering off nuclei is presented in general. As an example, elastic photon scattering off the deuteron in the unretarded dipole approximation is considered using the LIT metho
d. The inversion of the integral transform is discussed in detail paying particular attention to the high-energy contributions in the resonance term. The obtained E1-polarizabilities are compared to results from the literature. The corresponding theoretical cross section is confronted with experimental results confirming, as already known from previous studies, that the E1-contribution is the most important one at lower energies.
The LIT method has allowed ab initio calculations of electroweak cross sections in light nuclear systems. This review presents a description of the method from both a general and a more technical point of view, as well as a summary of the results obt
ained by its application. The remarkable features of the LIT approach, which make it particularly efficient in dealing with a general reaction involving continuum states, are underlined. Emphasis is given on the results obtained for electroweak cross sections of few--nucleon systems. Their implications for the present understanding of microscopic nuclear dynamics are discussed.
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