Phys. Med. Biol., 1980, Vol. 2 5 . No. 4, 637-649. Printed in Great Britain

Neutron cross-sections and kerma values for carbon, nitrogen and oxygen from 20 to 50 MeV

P J Dimbylow National Radiological Protection Board, Harwell, Didcot, Oxon. OX11 ORQ, England

Received 22 June 1979, in final form 14 December 1979

Abstract. The advent of high energy neutron radiotherapy will require the neutron cross-section data and kerma factors for elements of biomedical importance to be extended up to and possibly above 50 MeV. Nuclear model calculations have been employed to produce a set of neutron cross-sections for C, N and 0 from 20 to 50 MeV. The strategy employed involves the optical model fitting of experimental total cross-sections to produce elastic and non-elastic cross-sections. The non-elastic cross-section is then used to normal- ise the individual reaction cross-sections and charged particle spectra produced by the statistical model of level densities. Kerma values are obtained from charged particle and recoil nucleus spectra. A comparison is made with other kerma calculations, based on the intranuclear cascade-evaporation model, which are consistently lower than the results presented in this paper.

1. Introduction

Neutron cross-section data are the basic input for many types of calculation used in radiological protection, e.g. checking designs of shields and collimators by Monte Carlo and discrete ordinate methods, estimates of the distribution of dose and neutron spectra within the human body irradiated by broad and narrow beams, the conversion of neutron spectra into microdose distributions and the calculation of kerma per unit fluence in biological materials and in the materials from which dosemeters are made. Consequently, it is important to have available a set of evaluated neutron cross-section data. At present there is a wealth of information up to 20 MeV but above this energy there are very few experimental data. However, the advent of high energy neutron radiotherapy has created a need to extend the energy range of cross-section data for the main constituents of tissue besides hydrogen, i.e. carbon, nitrogen and oxygen from the present limit of 20 MeV, provided by the ENDF/B-IV evaluations (Lachkar eta1 1975, Foster and Young 1972, Young and Foster 1972) up to and possibly above 50 MeV.

Because of the scarcity of data between 20 and 50 MeV, nuclear model calculations have to be employed to provide the required cross-sections. The methods most appropriate are the optical model, the statistical model, precompound emission and direct reactions. The main reaction mechanism in this energy range is the statistical decay of the compound nucleus. However, the emission of the first particle from a target nucleus before statistical equilibrium is attained (precompound emission) becomes increasingly prominent as the neutron energy rises. Also direct reactions are important in the excitation of low lying levels particularly for the (n, n’) and (n, p) reactions. The problem with including precompound emission and direct reactions is that in order to evaluate their relative importance with regard to the statistical model, detailed experimental data on differential cross-sections and spectra are required; these are not available for C, N and 0. The method of calculating reaction cross-sections in

0031-9155/80/040637+ 13$01.00 @ 1980 The Institute of Physics 637

638 P J Dimbylow

this paper is a first order approach where precompound emission and direct reactions are not considered. Also, low lying energy levels are not treated separately in the statistical model but as part of a continuum of levels. The strategy employed was to fit the experimental total cross-section data (which are virtually the only data available between 20 and 50 MeV) and ENDF/B-IV elastic and non-elastic data below 20 MeV for C, N and 0 using the optical model. The calculated non-elastic cross-sections obtained were then used to normalise the individual reaction cross-sections calculated by the statistical model. The parameters chosen in the optical and statistical model calculations are not unique and changing these parameters will result in variations in the cross-sections and kerma values. It is difficult to assess the errors involved without experimental data for comparison. However, the setting of these parameters by mainly fitting data below 20 MeV results in values presented here at the lower energies being more credible than those at the higher energies, since the uncertainties will increase with rising neutron energy.

This paper describes the nuclear models and the reaction kinetics used to convert the charged particle and recoil nucleus spectra into kerma. Neutron cross-sections and kerma factors are presented, the latter being compared with previous calculations of Alsmiller and Barish (1977) and Wells (1978) using the intranuclear cascade plus evaporation model. The assumptions which underly the calculations are discussed and areas where further study is required are suggested.

2. Nuclear model calculations

2.1 Optical model

The optical model derives its name by analogy with the scattering and absorption of light. The presence of a complex optical potential, representing the nucleus, changes the wavelength of nucleons incident on the nucleus and thus provides a macroscopic refractive index for the nucleons. The real part of the complex potential represents elastic scattering and the imaginary part describes non-elastic processes permitted by the Pauli principle and conservation of energy.

An optical model computer program, NOPTIC (Dimbylow 1978b) based on the method of Buck et a1 (1960) has been written. The optical potential used is of the form

VopT= Vf(r)+iWg(r)+ V,,l.sh(r) (1)

where V and W are the real and imaginary depths of the central potential and V,, is the depth of the spin-orbit potential. The radial dependence of the potentials is described by the form-factors f(r), g(r) and h(r). The real form-factor f(r) is the widely adopted Saxon-Woods shape, g(r) is a surface-peaked Gaussian and the spin-orbit factor is taken as a derived Saxon-Woods shape:

2 d r dr

/I (r) = -- - (1 + exp[(r - ~ , , ) / a ~ ~ ] } ” .

R and a represent effective nuclear radii and surface diffuseness parameters respec- tively. The nine independent parameters of this optical potential were reduced by using

Neutron cross-sections and kerma values for C, N a n d 0

the following global values (Dimbylow 1978a):

R = R , = R,, = 1-23 A1j3 fm

a , = 1.2 fm

a = 0.6 fm for C and N; 0.65 fm for 0

V,, = -7.0 MeV.

639

The problem now consists of finding suitable values for V and W as a function of the incident neutron energy. At 20 MeV the calculations were matched to the ENDF/B- IV data for C, N and 0. The results of this matching are shown in table 1.

Table 1. Comparison between ENDF/B-IV and calculated total and elastic cross-sections at 20 MeV (cross-sections in mb).

ENDF/B-IV This work Element TOT EL TOT UEL

C 1497 1031 1480 948 N 1550 984 1549 983 0 1668 1072 1668 1073

~ ~~ ~~

A problem arises in the calculation of total and elastic cross-sections for carbon at 20 MeV because of the presence of a broad structure in the elastic scattering cross- section at 19.5 MeV. Consequently in fitting the ENDF/B-IV elastic cross-section data a compromise must be made between the high value at 20 MeV and the general trend of the data below 20 MeV. W was set to -7 MeV at 50 MeV neutron energy and the total cross-section data at this energy were fitted by varying K Having obtained ‘anchoring points’ at 20 and 50 MeV a linear interpolation of V and W was used to calculate the total and reaction cross-sections at intermediate energies. For oxygen, however, linear interpolation produces total cross-sections which appear to be too high from 20 to 35 MeV. This was remedied by increasing the absolute value of W slightly more rapidly from 20 to 35 MeV. The real and imaginary potential depths used were as follows:

C: V = (10.35E - 1432*5)/30; W = -(0*3E + 195)/30 (6)

N: V = (12E - 1545)/30; W = -(0*5E + 185)/30 (7)

0: V = -0*04037E2 + 2-70035E - 80.859, E S 35 MeV;

V = 0.29E - 45.95, E > 35 MeV;

W = -(E + 160)/30. (8)

These prescriptions differ from the previous calculation presented in Dimbylow (1978a) in that the increase in the imaginary depth has been reduced (i.e. W = -7 not -1 1 MeV at 50 MeV neutron energy). This produces a smaller reaction cross-section which is more in accord with the non-elastic cross-section data for carbon obtained by MacGregor er ai (1958) from 20 to 30 MeV. The total and non-elastic cross-sections are given in table 2. Figure 1 shows calculated and measured total cross-sections for C and 0.

640 P J Dimbylow

Table 2. Total and non-elastic cross-sections (mb) for C, N and 0 from 20 to SO MeV.

Carbon Nitrogen Oxygen E (MeV) UTOT UNONEL UTOT uNONEL uTOT uNONEL

20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 so

1480 S31 1449 S09 1415 490 1380 473 1344 459 1307 446 1269 434 1231 423 1193 413 1156 404 1119 396 1083 388 1047 380 1013 374 980 367 948 361

1.550 1543 1530 1510 1485 1455 1422 1387 1351 1313 1274 1236 1197 1159 1122 1085

S66 545 521 511 496 482 469 458 448 438 429 42 1 414 406 400 394

1669 595 1681 S71 1666 550 1637 S32 1600 S16 1563 S03 1528 491 1500 482 1470 473 1433 465 1396 457 1359 449 1322 443 1286 437 1250 431 1216 426

0 E, 1 M e V )

Kpre 1. Calculated and experimental total cross-sections for carbon and oxygen from 20 to 50 MeV. .Bowen~t~l(1961);OBubberal1974;OCierjackseral1968;~HildebrandandLeith(1960);.Pete~~on et al 1960; + Taylor and Wood (1953); x West er a1 1965; * Auman er al 1972.

Neutron cross-sections and kerma values for C, N a n d 0 64 1

2.2 Statistical model of level densities (evaporation model)

The statistical model of level densities describes the formation and decay of a compound nucleus under the assumption that both the compound nucleus and the residual nucleus form a continuum of energy levels. A computer program, SMOLDERS (Dimbylow 1978b) based on this model has been developed to calculate the emission probabilities of n, p, d, t, 3He and &-particles for reaction chains of up to six sequentially produced compound nuclei. It is assumed the y-emission is negligible above the threshold for particle production. The excitation energy of the compound nucleus is divided into a grid with a mesh size of 0.5 MeV. The emission functions are obtained by summing the emission probabilities for each grid energy Vi, over all possible values of i. The Fermi gas model of level densities (see Gilbert and Cameron 1965) assumes a gas composed of neutrons and protons where the single particle levels are equidistant and nondegenerate. Averaged values for pairing energies have been taken from Vonach and Hille (1969). The inverse cross-sections for the formation of a compound nucleus by charged particles were taken from the work of Dostrowsky et a1 (1959) whose empirical formulation includes an approximate treatment of coulomb barrier penetra- tion.

The approach used in calculating non-elastic cross-sections was to fit known reaction data by adjustment of the level density parameters and then use these values to predict cross-sections for reactions which have no experimental data. The reaction cross-section data available, to be compared with statistical model predictions consist of (n, 2n) cross-sections above 20 MeV (Ackermann etal 1975, Brolley etal 1952, Brill et a1 1961) and the ENDFIB-IV evaluated files below 20 MeV. The reaction cross- sections cannot be fitted for each element in isolation because there are residual nuclei common to one or more reactions from different elements. e.g. the l60 (n, 0) 13C and

N (n, np) 13C reactions. Therefore all the known reaction data above 10 MeV for C, N and 0 were fitted simultaneously. The first approximation was to set all level density parameters to A/8, then, where necessary, level density parameters for individual nuclei were varied SO as to reproduce the experimental cross-sections. A detailed description of the fitting process is given in Dimbylow (1978a).

14

3. Reaction kinetics and the calculation of kerma values

Kerma is the sum of the initial kinetic energies of all the charged particles liberated by indirectly ionising particles.

If Nm (gi) is the number of particles of type m emitted with energies between ei - A E / ~ and ej + A E / ~ , where AE is the energy grid width, then kerma is given by

Kerma = c 1 N m ( e i ) e i A ~ m = p, d, t, a +recoil nuclei. (9) m i

A version SMOLDERS-K of the program SMOLDERS has been developed to convert centre-of-mass exit channel energies produced by the statistical model into particle and recoil nucleus spectra in the laboratory system from which kerma can be calculated. Multiple particle cascade chains (e.g. 16 0 (n, npnp) 13C) are treated as sequential two-body break-up reactions. In all processes the angular distribution of the emitted particles is assumed to be isotropic in the centre-of-mass system. The emission of the first particle is treated using the standard kinetics for a non-elastic reaction. (see e.g. Dennis 1973).

642 P J Dimbylow

Consider a neutron of mass m, and energy E, incident on a target nucleus, MT. A reaction occurs in which a particle, mP, is emitted with kinetic energy in the laboratory system. The recoil nucleus, MR has a laboratory kinetic energy and a residual excitation Vi. If the separation energy for the reaction is -Q, the centre-of- mass energy E? available to the exit channel is

E ~ m = [ M T / ( m n + M T ) ] E n + Q - U i . (10)

Then

= a 2 + b 2 + 2 a b cos 8 (11)

where

The recoil nucleus kinetic energy can be obtained from

€ ~ f € ~ = [ m , E , / ( m , + ~ ~ ) ] + € ~ ~ . (13)

8 is the scattering angle of the emitted particle in the centre-of-mass system. By definition of the statistical model of level densities the distribution of the emitted particle is isotropic in the centre-of-mass. Thus will be equidistributed from a minimum of (a - b)' to a maximum of (a + b)'. The laboratory distributions obtained for each are summed over i to produce the total laboratory spectra for the emitted particle and the recoil nucleus involved in that particular reaction. The part of the residual nucleus's excitation energy distribution which is high enough to allow the emission of a further particle will not contribute to the kerma from that residual nucleus because its kinetic energy will be transmitted to the products of its decay. Below the threshold for further particle decay it is assumed that the levels decay by the emission of y-rays (which do not contribute to kerma). The sequential emission of further particles (other than the first) is treated as though the compound nucleus collides with a massless target. The kinetics in this case are complicated by the compound nucleus having a distribution of kinetic energies. Thus, the laboratory spectra must be obtained by summing the individual laboratory distributions produced from all possible couplings of the compound nucleus kinetic energy with the reaction channel energy.

Consider the compound nucleus to have a mass M, and kinetic energy E,. Let a particle mp be emitted with laboratory kinetic energy leaving a recoil nucleus MR with kinetic energy E R . Then

E : ~ = U ~ + Q - U I (14)

giving

~ ~ = a ~ + b ~ + 2 a b cos 8

where

Vi is the initial excitation of the compound nucleus; Vi is the final excitation of the recoil nucleus; -Q is the separation energy for the reaction; E?" is the centre-of-mass

Neutron cross-sections and kerma values for C, N a n d 0 643

exit channel energy for the reaction; and 0 is the scattering angle of the emitted particle in the centre-of-mass.

As before, isotropy in the centre-of-mass gives €p varying linearly with cos 0 from (a - b)' to ( a +- b)'.

If a cascade chain reaches 'Be the sequence is terminated by the fission of 8Be into two a-particles. The contribution to kerma from this reaction is obtained from the kinetic energy of the 'Be nucleus, the internal excitation of 'Be and also a positive Q-value of +0.0919 MeV. It is assumed that the energy from these three sources is converted into the kinetic energy of the resulting a-particles.

The contribution to kerma from the elastic recoils of "C, 14N and l60 was computed using the Legendre polynomial coefficients given in Dimbylow (1978a).

4. Results

The relative importance of the various particles contributing to kerma for C, N and 0 at 20 and at 50 MeV are given in table 3.

Table 3. Percentage contributions to kerrna for C, N and 0.

Carbon Nitrogen Oxygen Species E = 2 0 M e V E = 5 0 M e V E = 2 0 M e V E = 5 0 M e V E = 2 0 M e V E =50MeV ~ ~~

P d t a l60 "N 14N l3C ' *C "B 'OB other recoils P

~~ ~~

1.0 0.7 - 79.1 - - - - 16.2

0.5 -

1.4

0.5

~~ ~~

15.3 11.0 2.9

58.6 - - - -

2.3 2.1 3.3 4 .4

0.1

26.9 10.3 4.4

20.5 - - 13.7 9 .2 4.5 4.8 1.4 4.3

-

17.9 16.3 6 .0

50.5 - -

1.9 0.3 3.4 1.1 0.7 1.6

0.3

9.1 2.4 0.1

46.0 15.0 3.5 0.1 1.1

22.2 - -

0.4

0.1

39.3 9.1 2.3

26.1 2.3 2.2 7.1 2.4 2.1 2.7 0.1 4.1

0 .2 ~~

The most important contribution to kerma in carbon is from the 3a break-up reactions. Any particle cascade sequence which reaches 'Be will terminate with the disintegration of 8Be into two a-particles. The ''C (n, na ) 'Be + 2a reaction dominates the non-elastic cross-section at the lower energies having a value of 330 mb at 20 MeV. The ''C (n, an) 8Be -* 2a mode becomes more prominent with increasing energy rising to 75 mb at 50 MeV neutron energy. Figure 2 portrays the cross-sections for these two processes from 20 to 50 MeV. The cross-section for the other possible process, i.e.

C (n, 2 a ) 'He+na is small in comparison. Proton emission from the 12C (n, p) ''B* and "C (n, np) "B* reactions becomes increasingly important as the incident neutron energy increases. After (n, na), the (n, np) mode is the most favoured way in which particle unstable states in C (produced by inelastic scattering) decay. The cross-section for the "C (n, np) "B* reaction rises to 65 mb at 50 MeV. The excited states in 12B decay almost exclusively via neutron emission. Deuteron production from the "C (n, d) "B* reaction gives a notable contribution to the total kerma at higher

12

12

644 P J Dimbylow

Oh0 30 LO 50 1 €,(MeV1

Figure 2. The 3 0 break-up reactions in carbon.

energies. The relative importance of elastic scattering decreases from 11.6% of the total kerma at 20 MeV to 2.3% at 50 MeV because as the neutron energy increases the forward-peaking of the scattered neutron distribution becomes more predominant, resulting in less energy being delivered to the recoil nucleus. Contributions to kerma from short-lived, induced &activity are small.

The majority of the favoured reactions for nitrogen proceed either via ''C (e.g. (n, npn) and (n, dn)) or via '*B (i.e. (n, a)) en route to 'Be (if sufficient energy is available) which terminates the chain by splitting into two a-particles. As for carbon, alpha particles are the pre-eminent source of kerma. At the lower energies the

N (n, a) ''B reaction is significant, whilst at the higher energies the 14N (n, nda) 'Be; N (n, dna) 'Be and 14N (n, adn) 'Be break-up reactions increase in importance.

Deuterons are produced in the 14N (n, d) 13C* reaction as well as in the 'nda' break-up reactions. The contribution of protons to kerma arises mainly from the 14N (n, p) 14C and 14N (n, np) 13C reactions. The most notable cascade sequence occurring in nitrogen is

14

14

14 N + n-14N + n'

I ' B e + a d L

a a

and is illustrated in figure 3. The two main 'families' of reactions for oxygen are (i) the 4a break-ups and (ii)

cascades of neutrons and protons via 14N to "C, The threshold for the 4a reaction is 15.44 MeV. The dominant mode of reaching 'Be is l60 (n, n2a) 'Be and the cross- section for this reaction has a maximum of 55 mb at 40 MeV. The high I 6 0 (n, na ) ''C cross-section is responsible for the large contribution of "C recoils to the kerma for oxygen. The high fraction of kerma due to protons arises predominantly from the 0 (n, np) "N* reaction. Figure 4 shows the cross-sections for the l60 (n, npnp) 13C

cascade chain and figure 5 the l60 (n, na ) "C and l60 (n, n2a) *Be cross-sections. A more detailed description of the calculated cross-sections is given in Dimbylow (1978a) but the values presented there must be renormalised to the non-elastic cross-sections given in table 2.

16

Neutron cross-sections and kerma values for C, N a n d 0

Figure 3. The cross-sections for the I4N(n, npna)*Be+ 2a cascade chain.

150

". n E - b

50-

E, ( M e V )

Figure 4. The cross-sections for the 160(n, npnp)13C cascade

z200- E - , b 1

l

chain.

645

Figure 5. The cross-sections for I60(n, na)I2C reaction and the 40 break-up of oxygen.

646 P J Dimbylow

Table 4. Kerma factors for H, C, N, 0 and tissue in Gym'.

Energy (MeV) Hydrogen Carbon Nitrogen Oxygen Tissue

20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

4.688 0.350 0.303 0.243 0.705 4.650 0.396 0.323 0.258 0.719 4.606 0.429 0.344 0.271 0,728 4.555 0.454 0.360 0.277 0.731 4.501 0.469 0.378 0.287 0.735 4.444 0.480 0.397 0.299 0.740 4.396 0.501 0.420 0.314 0.750 4.339 0.511 0.444 0.326 0.755 4.284 0.527 0.457 0.337 0.760 4.232 0.539 0.478 0.351 0.767 4,182 0.553 0.502 0.364 0.774 4.135 0.568 0.523 0.376 0.781 4.088 0,581 0.545 0.387 0.786 4.044 0.598 0.567 0.398 0.793 4.001 0.619 0,589 0.409 0.800 3.960 0.628 0.611 0.423 0.808

The kerma factors for H are taken from Fleming (1974) up to 30 MeV and from Bassel and Herling (1977) above 30 MeV. The calculated kerma factors (i.e. kerma per unit fluence) for C, N, 0 and tissue (10.1% H, 11.1% C, 2.6% N, 76.2% 0 by weight) are presented in table 4 and a comparison with other calculations is made in figure 6.

I ' I

€,(MeV1

Figure 6. Kerma per unit fluence for carbon, nitrogen, oxygen and tissue from 20 to 50 MeV. -this work; 0 Caswell er al (1977); 0 Wells (1978); 0 Alsmiller eta1 (1977).

Neutron cross-sections and kerma values for C, N a n d 0 647

The data of Caswell et a1 (1977) are based on ENDF/B-IV evaluations below 20 MeV and from 20 to 30 MeV they are estimated by an optical model analysis of total cross-sections and an extrapolation of the component partial reaction cross-sections at 20 MeV up to 30 MeV. The calculations of Alsmiller and Barish (1977) and of Wells (1978) are based on the intranuclear cascade plus evaporation model. The basic assumptions in calculations of intranuclear cascades is that nuclear reactions involving particles of high energy can be described in terms of particle-particle collisions within the nucleus. The justification for this assumption is that the wavelength of the incoming particle and subsequent collision products is of the order of or smaller than the average internucleon distance within the nucleus. This occurs for energies greater than about 100 MeV, so the applicability of this model will lessen with decreasing neutron energy. When the intranuclear cascade has excited the nucleus into a compound state, the particle evaporation phase takes over.

The kerma factors calculated in this paper agree well at 20 MeV with the data of Caswell et a1 which are based up to this energy primarily on experimental cross- sections. The values obtained by Alsmiller and Barish for C, N and 0 are systematically lower than the results presented in this paper and the data of Caswell et a1 at 20 MeV. The results of Wells, although agreeing quite well for C and N at 20 MeV are lower than the calculated values at 50 MeV. The discrepancy between the various values for tissue is not so marked because of the relative importance of hydrogen coupled with the greater accuracy and plenitude of the hydrogen cross-section data.

5. Discussion

Most of the experimental cross-section data (few though they are) can be described within the framework of the nuclear models used. The optical model results are in favourable agreement with the experimental total cross-sections and with the ENDF/B-IV total and elastic data at 20 MeV. This goodness of fit and similarity of the optical model parameters used for C, N and 0 suggest that it is reasonable to apply the optical model to nuclei of low atomic mass. In general there is agreement between ENDF/B-IV and calculated cross-sections for first and possible second particle emis- sion below 20 MeV. On the basis of the level density parameters obtained from this fitting, the higher order reactions are calculated but without experimental data it is difficult to predict an error on their values.

The choice of the statistical model of level densities to describe reaction mechanisms has involved the simplifying assumptions that there is no pre-compound emission and that the residual nuclei energy levels form a continuum. Also any direct component to the reaction cross-sections has been ignored. Pre-equilibrium processes are described by the exciton model (Griffin 1966) where after the bombardment of a nucleus by a neutron the compound system starting with a small number of degrees of freedom is gradually transformed into a more complex configuration until statistical equilibrium is reached, i.e. the state of the compound nucleus. At high incident neutron energies it is more probable that the emission of the first and possibly the second particle will leave the residual nucleus with a high excitation energy well above the discrete energy level domain, although at the end of a cascade chain the residual nucleus will have a low excitation and a discrete level description would be more apt. Thus it would have been better to conjoin a continuum treatment of levels at the higher excitation energies with a set of discrete energy levels at low excitation, after the equilibration of the target nucleus by pre-compound processes. Direct reaction mechanisms are important in the

648 P JDimbylow

excitation of low lying levels particularly for the (n, n’) and (n, p) reactions and as the neutron energy increases so will their relative contribution to the non-elastic cross- section.

The errors involved in calculating kerma values arise from uncertainties in the neutron cross-sections used and the reaction kinetics applied to these cross-sections. One very critical quantity in the calculation of kerma is the non-elastic cross-section which is used to normalise the individual reaction cross-sections. Because there are virtually no experimental non-elastic cross-sections from 20 to 50 MeV, it is necessary to rely on the optical model fitting of total cross-sections to provide reasonable non-elastic cross-sections. The setting of statistical model parameters by mainly fitting data below 20 MeV results in the uncertainties on the cross-section data increasing with rising neutron energy. The 3a break-up reactions contribute most of the kerma for carbon and it is necessary to appraise the relative importance of the two major sequences of decay, because if a neutron is emitted first it will on average have more energy than if it is the second or third emitted particle in the break-up sequence. Therefore, the ”C (n, na) 8Be reaction will contribute less to kerma than

C (n, an ) 8Be per unit cross-section at a particular energy. Similarly, break-up reactions in N and 0 terminating in the fission of 8Be have an essential role. This means that kerma values for C, N and 0 are very sensitive to the description of the reaction mechanisms involved in reaching 8Be, notably for the I2C* + 8Be* +a and ’Be* + Be* + n processes. Because 12C, ’Be and 8Be have few energy levels (especially ‘Be) at

low excitation energies, a discrete level description of the compound nuclear decay for these modes would be more appropriate than the continuum description used. A further problem is that these break-up reactions might occur not by the sequential two-body processes postulated but by an explosive three or four particle dis- tintegration. The inclusion of direct reaction components, in inelastic scattering, which will preferentially excite the lower energy levels means that less of the incident neutron energy will be available to the residual nucleus produced by the inelastic scattering and so will tend to reduce the kerma.

It is hoped in future to explore the effects of including pre-equilibrium processes, discrete levels and direct reaction mechanisms on the cross-sections and kerma values for C, N and 0 and also to extend this work to other elements of biomedical importance such as Ca, P and S, and to elements of importance in dosemeter design such as Al, Mg and Ar.

12

8

Acknowledgments

I would like to thank Dr J A Reissland for his help and support, and the CEC who partly funded this work under contract no. 164-76-1 B10 UK.

R6sum6

Coupes transversales de neutrons et valeurs kerma du carbone, de l’azote et de I’oxygbne de 20 B 50 MeV.

L’introduction de radiothtrapie B neutrons de haute tnergie ntcessitera l’extension des donntes de coupe transversale de neutrons et des facteurs kerma des Cltments d’importance biomtdicale jusqu’h et peut-6tre au deli de 50 MeV. Des calculs de modkle nucltaire ont t t t utilists pour produire un jeu de coupes transversales de neutrons pour C, Net 0 de 20 B 50 MeV. La strattgie utiliste met en jeu l’adaptation d’un modble optique de coupes transversales totales exptrimentales pour produire des coupes transversales Clastiques et non tlastiques. La coupe transversale non tlastique est ensuite utiliste pour normaliser les coupes transversales de rtaction individuelle et le spectre de particules chargtes produites par le modble statistique des niveaux de

Neutron cross-sections and kerma values for C, N a n d 0 649

densitt. Les valeurs kerma sont obtenues B partir des spectres de particules chargtes et de recul nucltaire. Elles sont ensuite compartes B d'autres calculs de kerma, basts sur le modble de cascade-ivaporation intrancultaire, qui sont sans exception inftrieurs aux risultats prtsentts dans cet article.

Zusammenfassung

Querschnitte von Neutronen und Kerma-Werte fur Kohlenstoff, Stickstoff und Sauerstoff mit Energiewerten von 20 bis 50 MeV.

Mit dem Einsatz von Neutronen mit hohem Energiegehalt fur radiotherapeutische Zwecke mussen die Querschnittswerte fur die Neutronen und die GroPen der Kerma-Faktoren fur biomedizinisch bedeutsame Elemente bis auf 50 MeV und moglichenveise sogar auf noch hohrre Energiewerte ausgedehnt werden. Zur Erlangung einer Reihe von Neutronen-Querschnittswerte fur C, N und 0 im Energiebereich von 20 bis 50 MeV wurden an Hand von Kernmodellen Berechnungen durchgefuhrt. Die Vorgehensweise grundete sich auf der optischen Modellangleichung der experimentallen Gesamt-Querschnitte, um die elastischen und nicht-elastichen Querschnitte zu erhalten. Der nicht-elastische Querschnitt dient dann zur Normalisierung der verschiedenen Reaktions-Querschnitte und der Spektren der geladenen Teilchen, die durch das statistische Modell der Niveaudichten erzeugt werden. Die Kerma-Werte werden von den Spekktren der geladenen Teilchen und der abprallenden Kerne abgeleitet. Es wird ein Vergleich mit anderen Berech- nungsverfahren fur die Kerma-Werte angestellt, der auf dem intranuklearen Kaskadenverdampfungs- Modell beruht. Diese Werte sind durchgangig geringer als die in diesem Beitrag vorgetrangenen Werte.

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