An Innovative Approach to Construct Inverse Potentials Using Variational Monte-Carlo and Phase Function Method: Application to np and pp Scattering

Sastri, O. S. K. S.; Khachi, Anil; Kumar, Lalit

doi:10.1007/s13538-022-01063-1

Cited by 9 publications

(5 citation statements)

References 28 publications

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“…Multiplying s e s b ℓ ℓ throughout equation (8) and integrating from origin to asymptotic region one can find -¢…”

Section: Phase Function Methods For Manning-rosen Distorted Separable...mentioning

confidence: 99%

“…For solving quantum mechanical scattering issues, the Phase Function Method (PFM) [1,2] is both the most efficient and straightforward approach. This approach involves numerically solving the phase equation [3][4][5][6][7][8], a nonlinear differential equation of first-order, from origin to asymptotic region in order to produce the desired phase shifts. This effectively separates the wave equation's amplitude and phase components.…”

Section: Introductionmentioning

confidence: 99%

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Low and intermediate energy cross section analysis of p-p and p-d elastic scattering using modified phase amplitude method for electromagnetic distorted nuclear interaction

Swain,

Laha,

Behera

2023

Phys. Scr.

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The traditional phase function method is regarded as aresourceful tool for computing scattering phase shifts for quantummechanical potential scattering involving local interactions. For the localplus a nonlocal potential the conventional phase function method doesnot hold good. In such a situation one has to modify it. The modi edphase function method is adapted here to treat the Manning-Rosen plusGraz nonlocal separable potential for constructing an exact expression forthe phase function with rigorous inclusion of the electromagnetic e ect.The merit of our analytical result is demonstrated by computing elasticscattering phase parameters and differential scattering cross sections forproton-proton (p- p) and proton-deuteron (p-d) systems which are insensible agreement with previous works.

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“…Multiplying s e s b ℓ ℓ throughout equation (8) and integrating from origin to asymptotic region one can find -¢…”

Section: Phase Function Methods For Manning-rosen Distorted Separable...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Low and intermediate energy cross section analysis of p-p and p-d elastic scattering using modified phase amplitude method for electromagnetic distorted nuclear interaction

Swain,

Laha,

Behera

2023

Phys. Scr.

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“…On the contrary, this is a complex and computationally very demanding multi-step procedure that has to be performed with utmost accuracy'. We have constructed inverse potentials for S-waves of np [25], nd [26], S, P and D-states of nα [27] and αα [28] scattering by numerically solving the phase equation with the Morse function chosen as a zeroth reference. Based on the constructed inverse potentials using RPA for np interaction [25], we have determined deuteron's static properties, low energy scattering properties, analytical wave function for its ground state and its various electromagnetic form factors [29].…”

Section: Introductionmentioning

confidence: 99%

“…We have constructed inverse potentials for S-waves of np [25], nd [26], S, P and D-states of nα [27] and αα [28] scattering by numerically solving the phase equation with the Morse function chosen as a zeroth reference. Based on the constructed inverse potentials using RPA for np interaction [25], we have determined deuteron's static properties, low energy scattering properties, analytical wave function for its ground state and its various electromagnetic form factors [29]. One major advantage of RPA is, it directly constructs inverse potential based on the choice of mathematical function.…”

Section: Introductionmentioning

confidence: 99%

Inverse potentials for all ℓ channels of neutron-proton scattering using reference potential approach

et al. 2023

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Reference potential approach (RPA) is successful in obtaining inverse potentials for weakly bound diatomic molecules using Morse function. In this work, our goal is to construct inverse potentials for all available l-channels of np-scattering using RPA. The Riccati-type phase equations for various l-channels are solved using 5th order Runge-Kutta method to obtain scattering phase shifts (SPS) in tandem with an optimization procedure to minimize mean squared error (MSE). Interaction potentials for a total of 18 states have been constructed using only three parameter Morse interaction model. The obtained MSE is < 1% for 1S0, 3P1 and 3D1 channels and < 2% for 1P1 channel and < 0.1% for rest of the 14 channels. The obtained total scattering cross-sections at various lab energies are found to be matching well with experimental ones. Our complete study of np-scattering for all l-channels using RPA using Morse function as zeroth reference, is being undertaken for the ﬁrst time.

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“…In essence, they have replaced Hulthen function with a more generic version by using Manning-Rosen potential as a model of interaction for screened and cut-off Coulomb interaction. On the other hand, we have proposed a computational approach to construct inverse potentials [14,15] based on phase function method (PFM) in tandem with an optimisation utilising Variational Monte-Carlo (VMC) technique. This is akin to physics informed machine learning [16] wherein one obtains the inherent model from available data, either using a global optimisation algorithm [17] or neural networks [18], which is guided by the governing physical laws.…”

Section: Introductionmentioning

confidence: 99%

Constructing Inverse Scattering Potentials for α-α System using Physics Informed Machine Learning

sastri,

Sharma,

Awasthi

2023

Preprint

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An accurate way to incorporate long-range Coulomb interaction alongside short-range nuclear interaction remains challenging for theoretical physicists till date. Machine learning algorithms for global optimization, with physics equations guiding the process, are able to obtain robust models from available experimental data. In this article, we utilize the phase equation, which requires only potential and scattering energies as inputs, to obtain scattering phase shifts for the alpha-alpha system to construct the inverse potentials for its S, D, and G states. By incorporating the phase equation within an iterative loop of optimization code, mean absolute percentage error(MAPE) is minimized to obtain the best model parameters for a chosen reference potential. The key to successfully incorporating Coulomb interaction is in designing a reference potential. Here, a combination of two smoothly joined Morse functions, one regular followed by an inverted one, is considered. While the former takes care of short-range nuclear and Coulomb interactions, the latter accounts for expected barrier height due to the long-range Coulomb part that dominates once nuclear interaction subsides. The constructed inverse potentials for S, D, and G states have resulted in MAPE of 0.9, 0.5, and 0.4 and resonances(experimental) at 0.1240(0.0918), 2.95(3.03), and 11.89(11.35) respectively.

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An Innovative Approach to Construct Inverse Potentials Using Variational Monte-Carlo and Phase Function Method: Application to np and pp Scattering

Cited by 9 publications

References 28 publications

Low and intermediate energy cross section analysis of p-p and p-d elastic scattering using modified phase amplitude method for electromagnetic distorted nuclear interaction

Low and intermediate energy cross section analysis of p-p and p-d elastic scattering using modified phase amplitude method for electromagnetic distorted nuclear interaction

Inverse potentials for all ℓ channels of neutron-proton scattering using reference potential approach

Constructing Inverse Scattering Potentials for α-α System using Physics Informed Machine Learning

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