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Register a new userThe Lorentz Integral Transform and its Inversion
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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 historical 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.
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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 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 obtained 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.
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 method. 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 approach is tested for the calculation of astrophysical S-factors. As an example the S-factor of the reaction 2H(p,gamma)3He is considered. It is discussed that a sufficiently high density of LIT states at low energies is necessary for a precise determination of S-factors. In particular it is shown that the hyperspherical basis is not very well suited for such a calculation and that a different basis system is much more advantageous. A comparison of LIT results with calculations, where continuum wave functions are explicitly used, shows that the LIT approach leads to reliable results. It is also shown how an error estimate of the LIT inversion can be obtained.
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