A Monte Carlo C-code for calculating transmission efficiency of recoil separators and viewing residue trajectories

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Abstract

We present a semimicroscopic Monte Carlo code for calculating absolute transmission efficiency of recoil separators for heavy ion-induced complete fusion reactions. The code generates realistic distributions for energy, charge state and angle of evaporation residues. Residue trajectories are calculated using first order ion optical transfer matrices. Trajectory plots in the dispersive and the non-dispersive planes are generated. Using this code, we have obtained good agreement between calculated and measured transmission efficiencies for the Heavy Ion Reaction Analyzer at IUAC. The code can be adapted easily to any other electromagnetic recoil separator.

Program summary

Program title: TERS

Catalogue identifier: AEBD_v1_0

Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEBD_v1_0.html

Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland

Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html

No. of lines in distributed program, including test data, etc.: 6818

No. of bytes in distributed program, including test data, etc.: 1 216 097

Distribution format: tar.gz

Programming language: C

Computer: The code has been developed and tested on a PC with Intel Pentium IV processor

Operating system: Linux

RAM: About 8 Mbytes

Classification: 17.7

External routines: pgplot graphics subroutine library [1] should be installed in the system for generating residue trajectory plots.

Nature of problem: Recoil separators are employed to select and identify nuclei of interest, produced in a nuclear reaction, rejecting unreacted beam and other undesired reaction products. It is important to know what fraction of the selected nuclei, leaving the target, reaches the detection system. This information is crucial for determining absolute cross section of the studied reaction.

Solution method:Interaction of projectiles with target nuclei is treated event by event, semimicroscopically. Position and angle (with respect to beam direction), energy and charge state of the reaction products are calculated by Monte Carlo method. Trajectory of each nuclei inside the separator is then calculated by ion optical transfer matrix method. Ratio of the number of trajectories completing their journey up to the detection system to the total number of trajectories is a direct measure of absolute transmission efficiency of the separator.

Restrictions: The present version of the code is applicable to complete fusion reactions only. The code can be applied to other types of reactions (e.g., few nucleon transfer) as well, by suitably modifying energy and angular distribution of reaction products. Also, ion optical specifications and acceptance are unique for each recoil separator. Transmission efficiency calculation has been done for a specific recoil separator, viz. the Heavy Ion Reaction Analyzer [2,3] at IUAC. One has to make necessary changes in the code, while performing calculations for other recoil separators. Further, atomic number of the residual nucleus should not exceed 92, as the method used for calculating stopping power of ions [4] is valid for Z92.

Running time: From few seconds to several minutes depending on the reaction, number of events and separator layout.

References:

  • [1]

    http://www.astro.caltech.edu/~tjp/pgplot/.

  • [2]

    A.K. Sinha, N. Madhavan, J.J. Das, P. Sugathan, D.O. Kataria, A.P. Patro, G.K. Mehta, Nucl. Instr. Methods A 339 (1994) 543.

  • [3]

    S. Nath, Nucl. Instr. Methods A 576 (2007) 403.

  • [4]

    J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, vol. I, Pergamon Press, Oxford, 1984.

Introduction

In heavy ion-induced complete fusion reactions, residues formed via evaporation of light particles from the compound nuclei (CN), peak around 0° with respect to the beam direction. Therefore, those are submerged in the intense primary beam background and transfer reaction products. Recoil separators [1] select residues rejecting other abundant reaction products and transport those to the focal plane for clean and unambiguous identification. This task is accomplished by applying optimized electric and magnetic fields. In the operation of any recoil separator, one of the most important aspects is its transmission efficiency. This is an integral ingredient in the determination of absolute reaction cross section. Also, for proper planning and execution of an experiment in a recoil separator, one must estimate transmission efficiency for the proposed system beforehand.

In this paper we report a semimicroscopic Monte Carlo code, TERS, for calculating Transmission Efficiency of Recoil Separators. The code also generates residue trajectory plots in the dispersive and the non-dispersive planes. As an illustration, we have applied the code for transmission efficiency calculation of the Heavy Ion Reaction Analyzer (HIRA) [2] at IUAC. However, the code, with suitable modification, can be applied to any other recoil separator which uses electromagnetic fields for separation and identification of residues.

The paper is organized as follows. Section 2 describes briefly the model used in developing the code and the flow diagram. The code description is given in Section 3. A test run with typical input and output is presented in Section 4.

Section snippets

The model and the flow diagram for the computer code

The model used in developing the code is described in detail in Ref. [3]. Therefore, we present here only a few important formulae, necessary to understand the code. Flow diagram of the calculational procedure is given in Fig. 1. Transmission efficiency is calculated in two steps. First, for each residue six parameters are calculated viz. x, θ, y, ϕ, E, q, where x, θ and y, ϕ are displacement and divergence in the dispersive (xz) and the non-dispersive (yz) planes, respectively (z is the beam

The code

The code consists of four C program files and five input files. It produces seventeen output files. A list of files with brief description is presented below.

Test run

Here we show an example of transmission efficiency calculation for the complete fusion reaction 16O + 184W, studied in HIRA, at Ebeam=100MeV leading to the compound nucleus 200Pb [12]. We consider 5 neutron evaporation in the exit channel and 105 events. Following are the input parameters (in file ters_pti.inp) for the program ters_pti.c for performing projectile–target interaction calculation.

Generated distributions of residue angle, energy and charge state for this system are shown in Fig. 2.

Acknowledgement

The author is thankful to E.T. Subramanium for useful programming tips.

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This paper and its associated computer program are available via the Computer Physics Communications homepage on ScienceDirect (http://www.sciencedirect.com/science/journal/00104655).

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