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

Computer Physics Communications 179 (2008) 492–500

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Computer Physics Communications www.elsevier.com/locate/cpc

A Monte Carlo C-code for calculating transmission efficiency of recoil separators and viewing residue trajectories ✩ S. Nath Inter University Accelerator Centre, Aruna Asaf Ali Marg, Post Box 10502, New Delhi 110067, India

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 5 October 2007 Received in revised form 6 April 2008 Accepted 13 April 2008 Available online 24 April 2008 PACS: 02.70.Uu 29.30.h 25.70.Jj 41.85.p

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

Keywords: Monte Carlo simulation Recoil separator Complete fusion reaction Ion optics Transmission efficiency

✩ This paper and its associated computer program are available via the Computer Physics Communications homepage on ScienceDirect (http://www.sciencedirect. com/science/journal/00104655). E-mail address: [email protected].

0010-4655/$ – see front matter doi:10.1016/j.cpc.2008.04.014

©

2008 Elsevier B.V. All rights reserved.

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nucleus should not exceed 92, as the method used for calculating stopping power of ions [4] is valid for Z  92. 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.

© 2008 Elsevier B.V. All rights reserved.

1. 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. 2. 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 (x–z) and the non-dispersive ( y–z) planes, respectively (z is the beam direction), E is residue energy and q is residue charge state. Next, trajectory of each residue is calculated with the parameters obtained in the first step as the starting point. The fusion-point is chosen randomly within the thickness of the target. Energy loss of the beam particle up to this point and that of the residue in the remaining target thickness is calculated following Ref. [4]. Kinetic energy and excitation energy of the CN are respectively given by kin E CN =

∗ E CN =

Ap

E LAB ,

(1)

E LAB + Q ,

(2)

A p + At At A p + At

where Q is the Q -value for CN formation and other symbols are self-explanatory. Adopting Fermi-gas prescription [5] for the nuclear level density, nuclear temperature is calculated by the expression 1 T

=

1 ∂ρ

ρ ∂ E∗

=−

1.25 E∗

 +

π 2 go

 1/ 2 (3)

,

6E ∗

where go is the single particle level density and 16 π 2 go = a is called the “level-density parameter”. K = A /a, the inverse level-density parameter, is fed to the code as input. Energy spectra of the particles (neutrons, protons and α s) emitted from the CN with temperature T follow Maxwellian distribution, which is given by N ( E ) dE = 



2

π (kT )3

E 1/2 exp −

E kT



dE ,

(4)

where k is Boltzmann’s constant. After the first particle is boiled-off, the residual nucleus is left with an excitation energy ∗ E residual = E ∗ − S part − E part ,

(5)

where S part is the particle-separation energy and E part is kinetic energy of the emitted particle. For a given exit channel, the evaporation cascade is continued up to the last particle with a mandatory check on excitation energy (E ∗ > 0) after each evaporation. Particle evaporation is assumed to be isotropic in the frame of the CN. Each evaporation causes angular deviation of the residue from the beam direction. Angular deviation of residues caused by multiple small angle Coulomb scattering is assumed to be Gaussian, i.e. P (ϑ) dϑ ≈

2ϑ

ϑ2



exp −

 ϑ2 dϑ. ϑ 2 

(6)

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S. Nath / Computer Physics Communications 179 (2008) 492–500

Fig. 1. Schematic flow diagram of the calculational procedure of TERS.

The parameter ϑ2 represents the mean squared scattering angle which is evaluated following the method described in Ref. [6]. The resultant polar angle, from these two contributions, is converted to in-plane angle θ and out-of-plane angle φ , choosing the azimuthal angle with uniform distribution in the range 0 to 2π . A circular spot is assumed for the incident beam and x and y are generated within that spot-size with uniform probability. Residue charge states are calculated using formulae available in literature [7,8]. Using first order transfer matrices [9,10] trajectory of each residue is calculated. Trajectories are calculated in small steps, typically ∼1.0 cm to ensure that they are true representations of the actual ion paths inside the separator. After every step, each trajectory is subjected to checks dictated by apertures, vacuum chamber dimensions and finally the focal plane detector size. Trajectories which survive all these checks are counted and the transmission efficiency is defined simply by

=

no. of residues reaching the focal plane detector no. of residues emerging from the target

× 100%.

(7)

3. 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. 3.1. Program files 3.1.1. ters_pti.c This program performs projectile–target interaction calculation semimicroscopically. Residues with realistic position, angle, energy and charge state are produced event by event. There are several special functions in this program to perform specific jobs. Following is a list of functions with brief description.

double dedx() — Calculates and returns total stopping power of ions [MeV/(mg/cm2 )] based on the method described in Ref. [4]. double EvapPartE() — Calculates and returns energy [MeV] of evaporated particles (n, p and α ) following Maxwellian distribution.

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int ERQ() — Calculates and returns residue charge states based on Refs. [7,8]. double GaussRand() — Calculates and returns random numbers with Gaussian distribution (μ = 0 and σ 2 = 1) using Box–Muller transformation.

double Weibull() — Calculates and returns polar angles [rad] of residues due to multiple small angle Coulomb scattering in the target, following Ref. [6] and using Weibull distribution. 3.1.2. ters_tra.c This program calculates residue trajectories inside the separator using first order transfer matrices [9,10]. (x, θ ) and (y, φ) coordinates of the residues as a function of z are calculated, starting from the target (z = 0) in small steps of z. After each step of calculation, trajectories are put to checks so that those are contained within the dimensions of vacuum chambers and other apertures. Calculation for a trajectory is terminated if it fails a check. When a trajectory survives all checks to reach the focal plane detector, the residue counter at the focal plane is incremented by 1. Finally, absolute transmission efficiency is calculated using Eq. (7). One must note here that the layout of each recoil separator is unique. Electromagnetic configuration, solid angle acceptance, dimensions of vacuum chambers and size of the focal plane detector vary from one separator to another. Therefore, a general program for calculating transmission efficiency of recoil separators must offer flexibility and ease of use. Trajectory calculation in each ion optical element is performed by a dedicated function. In its present form, TERS supports (i) drift space, (ii) magnetic quadrupole, (iii) magnetic dipole, (iv) electric dipole, and (v) aperture, which are the most commonly used elements in heavy ion recoil separators. The functions and their arguments are described in detail in Appendix A. One can build a separator inside this program, element by element, by calling these functions in proper order with relevant parameters as arguments. Following is the syntax for calling any of these functions:

Status = Function(argument list); if (Status == 0) continue; The functions return a value 1, if the residue completes its journey through the ion optical element or 0 otherwise. The statement “if (Status == 0) continue;” ensures that the given trajectory is not calculated any further in the event of Status == 0 and calculation for the next trajectory from target is started. We illustrate transmission efficiency calculation for a recoil separator taking HIRA [2] at IUAC as an example. HIRA is a recoil mass spectrometer with first order electromagnetic configuration Q-Q-ED-MD-ED-Q-Q, where Q , ED and MD stand for magnetic quadrupole, electric dipole and magnetic dipole respectively. TERS configuration for HIRA is given in Appendix B. One has to replace only this part of the program (commented as BUILD YOUR SEPARATOR inside the program) by a new set of function calls for another recoil separator. Because of its modular structure more ion optical elements can be added to the program by simply adding a function corresponding to that element. 3.1.3. ters_xzp.c and ters_yzp.c These two programs generate trajectory plots for residues, employing pgplot graphics subroutine library [11], in the dispersive and the non-dispersive planes, respectively. Layout of the electromagnetic elements with labels is also simulated by them. One must install pgplot in the system before compiling and running these programs. 3.2. Input files 3.2.1. ters_pti.inp This file contains input data required by the program ters_pti.c. Parameters specific to a particular reaction are defined here. We present below a list of the parameters with short explanation.

Zp, Ap, Zt, At — Atomic no. and mass no. of projectile and target. Ep — Projectile energy [MeV] in laboratory. BeamSpot, TarThick — Dia. [mm] of (circular) beam spot and target thickness [mg/cm2 ]. Qvalue, ILPM — Q value [MeV] for CN formation and inverse level density parameter. AlphaNo, ProtonNo, NeutronNo — Numbers of evaporated alphas, protons and neutrons. Salpha[] — Alpha separation energies [MeV], to be left blank if no alpha evaporation. Sproton[] — Proton separation energies [MeV], to be left blank if no proton evaporation. Sneutron[] — Neutron separation energies [MeV], to be left blank if no neutron evaporation. NEVENT — Number of events, i.e. residues to be considered by the program (maximum 5 × 105 ). Particle evaporation is performed sequentially in the order: α s, protons and neutrons. Since a mass table is not part of the program, one has to feed particle separation energies explicitly in the input file. 3.2.2. ters_tra.inp This file contains input data required by the program ters_tra.c. Separator settings for the system considered are defined here. A list of the parameters with short explanation is presented below.

A0 — Residue mass number. E0, A00, q0 — Energy [MeV], mass no. and charge state of the reference particle. NEVENT — Number of events, i.e. trajectories to be calculated.

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S. Nath / Computer Physics Communications 179 (2008) 492–500

Number of events here should be less than or equal to the number of events used for projectile–target interaction calculation, mentioned in Section 3.2.1. 3.2.3. ELEMDATA.DAT This file contains data on natural elements (up to Z = 92) [4], used by the function dedx() in the program ters_pti.c for calculating stopping power of ions. Contents of this file must not be changed. 3.2.4. PSCSCOEF.DAT This file contains proton stopping cross section coefficients in natural elements [4], used by the function dedx() in the program ters_pti.c for calculating stopping power of ions. Contents of this file must not be changed. 3.2.5. ECSPARAM.DAT This file contains parameters [8] used by the function ERQ() in the program ters_pti.c for calculating equilibrium charge states of residues with atomic number 53. Contents of this file must not be changed. 3.3. Output files The code produces the following four groups of output files. 3.3.1. Log files

ters_pti.log — Contains run log for the program ters_pti.c. ters_tra.log — Contains run log for the program ters_tra.c and calculated transmission efficiency. 3.3.2. Files produced by the program ters_pti.c and used as input by the program ters_tra.c for trajectory calculation — Contains residue x-coordinates [m]. — Contains residue θ -coordinates [rad]. — Contains residue y-coordinates [m]. — Contains residue φ -coordinates [rad]. — Contains residue energies [MeV]. — Contains residue charge states.

ters_rxc.dat ters_ria.dat ters_ryc.dat ters_roa.dat ters_ren.dat ters_rcs.dat

3.3.3. Files produced by the program ters_pti.c for generating histograms ters_ned.dat — Contains evaporated neutron energy [MeV] distribution data. ters_ped.dat — Contains evaporated proton energy [MeV] distribution data. ters_aed.dat — Contains evaporated alpha energy [MeV] distribution data. ters_rad.dat — Contains residue angular [deg.] distribution data. ters_red.dat — Contains residue energy [MeV] distribution data. ters_rcd.dat — Contains residue charge state distribution data. 3.3.4. Files produced by the program ters_tra.c ters_txz.dat — Contains (z, x) coordinates of residue trajectories which are used by the program ters_xzp.c for generating residue trajectory plot in the dispersive plane. ters_tyz.dat — Contains (z, y) coordinates of residue trajectories which are used by the program ters_yzp.c for generating residue trajectory plot in the non-dispersive plane. ters_xyp.dat — Contains data for generating two-dimensional position spectrum of residues at the focal plane of the separator. 4. Test run Here we show an example of transmission efficiency calculation for the complete fusion reaction 16 O + 184 W, studied in HIRA, at E beam = 100 MeV leading to the compound nucleus 200 Pb∗ [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.

8 16 74 184 100 5 0.210 -24.193 9 0 0 5 (blank line, as there is no alpha evaporation) (blank line, as there is no proton evaporation) 9.081 7.211 9.371 7.471 9.671 100000 Generated distributions of residue angle, energy and charge state for this system are shown in Fig. 2.

S. Nath / Computer Physics Communications 179 (2008) 492–500

Fig. 2. Calculated (a) angular, (b) energy and (c) charge state distributions of residues for the system 105 events.

16

O(100 MeV) +

497

184

W(210 μg/cm2 ). Calculations have been done for

For trajectory calculation, we consider 10 msr solid angle acceptance of HIRA and a detector of size 5 cm × 5 cm in the focal plane (see Appendix B). Following are the input parameters (in file ters_tra.inp) for the program ters_tra.c.

195 6.5 195 9 100000 The output on screen would look like the following:

Trajectory calculation starts at : Mon Feb 4 16:36:03 2008 **************************************** Total events = 100000 FP Count = 1250 Efficiency = 1.25 % **************************************** Trajectory calculation stops at : Mon Feb 4 16:37:03 2008 See program log in file ‘ters_tra.log’. Happy computing!

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S. Nath / Computer Physics Communications 179 (2008) 492–500

Fig. 3. Residue trajectory plot in the dispersive plane of HIRA for the system

16

Fig. 4. Residue trajectory plot in the non-dispersive plane of HIRA for the system

O+

16

184

O+

W.

184

W.

Residue trajectory plots in the dispersive and the non-dispersive planes are shown in Figs. 3 and 4, respectively. For clarity of view, only 2500 trajectories are drawn in both the plots.

Acknowledgement

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

S. Nath / Computer Physics Communications 179 (2008) 492–500

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Appendix A. Description of ion optical functions used in TERS (Table 1) Table 1 Description of functions used in the program ters_tra.c. Function names and the characters used in the argument lists are case sensitive Name of the function

Job of the function

List of arguments

Description of arguments

DriftLength()

To calculate trajectory in a drift space

double arg1, int arg2, double arg3, double arg4

arg1 = length of drift space [m] arg2 = shape of physical boundary: ‘C’ for circular, ‘E’ for elliptical, ‘R’ for rectangular arg3 = radius [m] if shape is ‘C’; semi major axis [m] if shape is ‘E’; half of the side [m] parallel to x-axis if shape is ‘R’ arg4 = unused if shape is ‘C’; semi minor axis [m] if shape is ‘E’; half of the side [m] parallel to y-axis if shape is ‘R’

MagQuad()

To calculate trajectory in a magnetic quadrupole

double arg1, double arg2, double arg3, int arg4 int arg5, double arg6, double arg7

arg1 arg2 arg3 arg4 arg5 arg6 arg7

= = = = = = =

effective length [m] aperture radius [m] pole-tip field [Tesla] plane of focusing: ‘X’ for same as arg2 in function same as arg3 in function same as arg4 in function

x–z plane; ‘Y’ for y–z plane

DriftLength() DriftLength() DriftLength()

MagDipole()

To calculate trajectory in a magnetic dipole

double arg1, double arg2, int arg3 double arg4, double arg5, int arg6, double arg7, double arg8

arg1 = bending radius [m] arg2 = bending angle [deg] arg3 = bending direction (looking downstream): ‘N’ for clockwise; ‘P’ for anti-clockwise arg4 = entrance edge angle [deg] arg5 = exit edge angle [deg] arg6 = same as arg2 in function DriftLength() arg7 = same as arg3 in function DriftLength() arg8 = same as arg4 in function DriftLength()

ElecDipole()

To calculate trajectory in an electric dipole

double arg1, double arg2, int arg3 int arg4, double arg5, double arg6

arg1 arg2 arg3 arg4 arg5 arg6

To check whether trajectories are within given limits

int arg1, double arg2, double arg3

arg1 = same as arg2 in function DriftLength() arg2 = same as arg3 in function DriftLength() arg3 = same as arg4 in function DriftLength()

Aperture()

= = = = = =

bending bending same as same as same as same as

radius [m] angle [deg] arg3 in function arg2 in function arg3 in function arg4 in function

MagDipole() DriftLength() DriftLength() DriftLength()

Appendix B. TERS configuration for HIRA Program segment from ters_tra.c to describe ion optical and geometrical configurations of HIRA [2] is shown below. The solid angle acceptance corresponding to the values used here, as the arguments of function Aperture() after the first drift space, is 10 msr. The detector at the focal plane is assumed to have an active area of 5 cm × 5 cm. Magnetic quadrupole fields are scaled from the values used in a particular experiment in HIRA. These values (stored in variables FQ1, FQ2, FQ3, FQ4) have been used as arguments while calling function MagQuad(). To configure another separator, numerical values of magnetic fields [T] should be used instead of these variables. More details about HIRA transmission efficiency calculation can be found in Ref. [3].

Status = DriftLength(0.360, ’C’, 0.250, 0.000); if (Status == 0) continue; Status = Aperture(’C’, 0.020, 0.000); // solid angle if (Status == 0) continue; // defining aperture Status = DriftLength(0.080, ’C’, 0.250, 0.000); if (Status == 0) continue; Status = DriftLength(0.060, ’C’, 0.054, 0.000); if (Status == 0) continue; Status = MagQuad(0.292, 0.060, FQ1, ’X’, ’C’, 0.054, 0.000); if (Status == 0) continue; Status = DriftLength(0.040, ’C’, 0.054, 0.000); if (Status == 0) continue; Status = DriftLength(0.078, ’E’, 0.044, 0.075); if (Status == 0) continue; Status = MagQuad(0.220, 0.060, FQ2, ’Y’, ’E’, 0.044, 0.075); if (Status == 0) continue; Status = DriftLength(0.100, ’E’, 0.044, 0.075); if (Status == 0) continue; Status = DriftLength(0.300, ’C’, 0.250, 0.000); if (Status == 0) continue; Status = ElecDipole(5.0, 16.0, ’N’, ’R’, 0.075, 0.200);

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S. Nath / Computer Physics Communications 179 (2008) 492–500

if (Status == 0) continue; Status = DriftLength(0.170, ’C’, 0.250, 0.000); if (Status == 0) continue; Status = DriftLength(0.834, ’R’, 0.110, 0.031); if (Status == 0) continue; Status = MagDipole(0.86, 36.3, ’P’, 7.17, 7.44, ’R’, 0.250, 0.031); if (Status == 0) continue; Status = DriftLength(0.574, ’R’, 0.110, 0.031); if (Status == 0) continue; Status = DriftLength(0.260, ’R’, 0.110, 0.250); if (Status == 0) continue; Status = DriftLength(0.170, ’R’, 0.075, 0.200); if (Status == 0) continue; Status = ElecDipole(5.0, 16.0, ’N’, ’R’, 0.075, 0.200); if (Status == 0) continue; Status = DriftLength(0.330, ’C’, 0.250, 0.000); if (Status == 0) continue; Status = DriftLength(0.070, ’C’, 0.068, 0.000); if (Status == 0) continue; Status = MagQuad(0.322, 0.075, FQ3, ’Y’, ’C’, 0.068, 0.000); if (Status == 0) continue; Status = DriftLength(0.070, ’C’, 0.068, 0.000); if (Status == 0) continue; Status = DriftLength(0.080, ’E’, 0.100, 0.055); if (Status == 0) continue; Status = MagQuad(0.427, 0.075, FQ4, ’X’, ’E’, 0.100, 0.055); if (Status == 0) continue; Status = DriftLength(0.100, ’E’, 0.100, 0.055); if (Status == 0) continue; Status = DriftLength(0.550, ’C’, 0.250, 0.000); if (Status == 0) continue; Status = Aperture(’R’, 0.025, 0.025); // focal plane if (Status == 0) continue; // detector Appendix C. Comparison between measured and calculated absolute transmission efficiencies of HIRA (Table 2) Table 2 Calculation for each system is done for 106 events. The table is reproduced from Ref. [3] System

Beam energy [MeV]

Target thickness

W

100

210

195

Pb, 5n

0.98 ± 0.05

1.27

Lu

110

200

188

Hg, 6n

1.78 ± 0.09

1.98

440

109

Sn, 3n Sn, 4n

0.49 ± 0.05 0.68 ± 0.07

0.49 0.61

Cd, 2pn Ag, 3pn Cd, 2pn 104 Cd, 2p2n 109 In, p2n 108 In, p3n

7.70 ± 1.70 4.60 ± 2.10 7.10 ± 1.5 6.10 ± 0.60 9.30 ± 2.60 11.70 ± 1.00

9.01 7.30 7.91 9.23 8.47 9.56

16

O+

184

19

F+

175

19

F+

93

Nb

68

[μg/cm2 ]

Exit channel

108

48

Ti +

58

48

Ti +

60

Ni

270

48

Ti +

64

Ni

240

Ni

160

330

103 102 105

Efficiency Measured [%]

Calculated [%]

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

C.N. Davids, Nucl. Instr. Methods B 204 (2003) 124. 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. S. Nath, Nucl. Instr. Methods A 576 (2007) 403. J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, vol. I, Pergamon Press, Oxford, 1984. A. Bohr, B.R. Mottelson, Nuclear Structure, vol. 1, World Scientific, Singapore, 1998. G.R. Lynch, O.I. Dahl, Nucl. Instr. Methods B 58 (1991) 6. V.S. Nikolaev, I.S. Dmitriev, Phys. Lett. A 28 (1968) 277. R.N. Sagaidak, A.V. Yeremin, Nucl. Instr. Methods B 93 (1994) 103. H. Wollnik, Optics of Charged Particles, Academic Press, Orlando, 1987. A.P. Banford, The Transport of Charged Particle Beams, E. & F. N. Spon Limited, London, 1966. http://www.astro.caltech.edu/~tjp/pgplot/. P.D. Shidling, N.M. Badiger, S. Nath, R. Kumar, A. Jhingan, R.P. Singh, P. Sugathan, S. Muralithar, N. Madhavan, A.K. Sinha, S. Pal, S. Kailas, S. Verma, K. Kalita, S. Mandal, R. Singh, B.R. Behera, K.M. Varier, M.C. Radhakrishna, Phys. Rev. C 74 (2006) 064603.