Background: An accurate way to incorporate long range Coulomb interaction alongside short-range nuclear interaction has been a challenge for theoretical physicists. Purpose: In this paper, we propose a methodology based on the reference potential approach for constructing inverse potentials of alpha-alpha scattering. Methods: Two smoothly joined Morse potentials, regular for short-range nuclear interaction and inverted for long range Coulomb, are used in tandem as a reference potential in the phase function method to obtain the scattering phase shifts for the S, D and G states of alpha-alpha scattering. The model parameters are optimized by choosing to minimize the mean absolute percentage error between the obtained and experimental scattering phase shift values. Results: The constructed inverse potentials for S, D and G states have resulted in mean absolute percentage errors of 0.8, 0.5, and 0.4 respectively. The obtained resonances for D and G states closely match the experimental ones. Conclusion: The reference potential approach using a combination of smoothly joined Morse functions is successful in accurately accounting for the Coulomb interaction between charged particles in nuclear scattering studies.

O. S. K. S. Sastri Arushi Sharma Ayushi Awasthi

We study the statistical properties of eigenvalues of the Hessian matrix ${\cal H}$ (matrix of second derivatives of the potential energy) for a classical atomic liquid, and compare these properties with predictions for random matrix models (RMM). The eigenvalue spectra (the Instantaneous Normal Mode or INM spectra) are evaluated numerically for configurations generated by molecular dynamics simulations. We find that distribution of spacings between nearest neighbor eigenvalues, s, obeys quite well the Wigner prediction $s exp(-s^2)$, with the agreement being better for higher densities at fixed temperature. The deviations display a correlation with the number of localized eigenstates (normal modes) in the liquid; there are fewer localized states at higher densities which we quantify by calculating the participation ratios of the normal modes. We confirm this observation by calculating the spacing distribution for parts of the INM spectra with high participation ratios, obtaining greater conformity with the Wigner form. We also calculate the spectral rigidity and find a substantial dependence on the density of the liquid.

Srikanth Sastry Nivedita Deo Silvio Franz

We use the anti-equivalence between Cohen-Macaulay complexes and coherent sheaves on formal schemes to shed light on some older results and prove new results. We bring out the relations between a coherent sheaf M satisfying an S_2 condition and the lowest cohomology N of its "dual" complex. We show that if a scheme has a Gorenstein complex satisfying certain coherence conditions, then in a finite \'etale neighborhood of each point, it has a dualizing complex. If the scheme already has a dualizing complex, then we show that the Gorenstein complex must be a tensor product of a dualizing complex and a vector bundle of finite rank. We relate the various results in [S] on Cousin complexes to dual results on coherent sheaves on formal schemes.

Suresh Nayak Pramathanath Sastry

Clustering is an important data mining technique where we will be interested in maximizing intracluster distance and also minimizing intercluster distance. We have utilized clustering techniques for detecting deviation in product sales and also to identify and compare sales over a particular period of time. Clustering is suited to group items that seem to fall naturally together, when there is no specified class for any new item. We have utilizedannual sales data of a steel major to analyze Sales Volume & Value with respect to dependent attributes like products, customers and quantities sold. The demand for steel products is cyclical and depends on many factors like customer profile, price,Discounts and tax issues. In this paper, we have analyzed sales data with clustering algorithms like K-Means&EMwhichrevealed many interesting patternsuseful for improving sales revenue and achieving higher sales volume. Our study confirms that partition methods like K-Means & EM algorithms are better suited to analyze our sales data in comparison to Density based methods like DBSCAN & OPTICS or Hierarchical methods like COBWEB.

S. Hanumanth Sastry Prof. M. S. Prasada Babu

Understanding neutron-proton(np) interaction has been one of the most studied problems. One way to construct model interaction has been using inversion potentials obtained from experimental scattering phase shifts(SPS). Here, we show that, inverse potentials corresponding to SPS for various l-channels of np interaction can be obtained using variational Monte-Carlo(VMC) technique in tandem with phase function method(PFM) by modeling np-interaction as a Morse function. The S-channel SPS for 3S1 and 1S0 have been obtained, with a mean percentage error with respect to experimental multiple energy analysis data for lab energies up to 1050 MeV, to less than 5%. Similarly, inverse potential for 1S0 pp interaction, with Coulomb term modeled as proportional to erf(), has also been obtained to match experimental values to less than 4%. Non-local and spin-orbit terms are included to obtain inverse potentials for P and D channels and results match with available data to a good extent.

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

In this paper, we determine deuteron's static properties, low energy scattering parameters, total cross-section and form factors from inverse S-wave potentials constructed using Morse function. The scattering phase shifts (SPS) at different lab energies are determined using phase function method. The model parameters are optimised using both machine learning algorithm and traditional data analysis by choosing mean squared error as cost function. The mean absolute error between experimental and obtained SPS for states 3S1 and 1S0 are found to be 0.35 and 0.70 respectively. The low energy scattering parameters are matching well with expected values. The contribution due to S-waves SPS towards total cross-section at various energies have been obtained and are matching well with experimental values. The analytical ground state deuteron wave-function (DWF) is obtained by utilizing the experimental value for Quadrupole moment. Other static properties and form factors determined from obtained DWF are found to be in close agreement with experimental ones.

Anil Khachi Lalit Kumar M. R. Ganesh Kumar O. S. K. S Sastri

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. This phase wave analysis study of all channels of np-scattering using RPA has been undertaken using Morse function as zeroth reference, by us, is for the first time.

Anil Khachi Lalit Kumar Ayushi Awasthi O. S. K. S. Sastri

The neutron-deuteron (nd) and proton-deuteron (pd) scattering are the simplest nucleon-nucleus scenario which throws light on understanding few body systems. In this work, real and imaginary parts of scattering phase shifts (SPS) for nd and pd scattering are obtained using optical potential, with Malfliet-Tjon (MT) model of interaction, by phase function method (PFM). The SPS for doublet 2S1/2 and quartet 4S3/2 states of nd and pd systems have been obtained for real and imaginary parts separately by solving the phase equation for l= 0, using Runge-Kutta 5 th order technique for laboratory energies up to 19 M eV . The obtained (real,imaginary) SPS for 2S1/2 and 4S3/2 states are matching with standard data with mean absolute error (MAE) of (1.32, 0.06) for 2S1/2 state and (0.19, 0.06) for 4S3/2 state of nd scattering, (1.47,0.62) for 2S1/2 state and (0.55, 0.14) for 4S3/2 state of pd scattering.

Shikha Awasthi O. S. K. S. Sastri

In this article, we propose a numerical approach to solve quantum mechanical scattering problems, using phase function method, by considering neutron-proton interaction as an example. The nonlinear phase equation, obtained from the time-independent Schrodinger equation, is solved using the Runge-Kutta method for obtaining S-wave scattering phase shifts for neutron-proton interaction modeled using Yukawa and Malfliet-Tjon potentials. While scattering phase shifts of S-states using Yukawa match with experimental data for only lower energies of 50 MeV, Malfliet-Tjon potential with repulsive term gives very good accuracy for all available energies up to 350 MeV. Utilizing these S-wave scattering phase shifts, low energy scattering parameters, and total S-wave cross section have been calculated and found to be consistent with experimental results. This simulation methodology can be easily extended to study scattering phenomenon using phase wave analysis approach in the realms of atomic, molecular, and nuclear physics.

Shikha Awasthi Anil Khachi Lalit Kumar O. S. K. S. Sastri

Background: The study of np and pp scattering, central to understanding nuclear force, remains an optional topic in many undergraduate nuclear physics curriculum. Purpose: The main thrust of this paper is to study pp scattering using the phase function method to obtain the observed S-wave phase shifts and cross-sections at various energies. Methods: The pp interaction has been modeled by choosing the Malfliet-Tjon potential for the nuclear part along with the screened Coulomb potential. The phase equation has been solved to obtain scattering phase shifts using the fourth-order RK method (RK-4). Results: The interaction potential obtained from optimized parameters matches well with the realistic Argonne V18 potential for 1S0 state of pp scattering and the scattering phase shifts as well as the cross-section for energies ranging from 1-350 MeV are in good agreement with expected data. Conclusion: Introducing the phase function method for S-wave (l=0) could bring this interesting study of nucleon-nucleon scattering to the undergraduate classroom.

Shikha Awasthi Anil Khachi O. S. K. S. Sastri