Memo to H Amols, Et Al, Subject: Pion 1 Calculation (Attach: Dose Perturbations at Interfaces Due to Pion Stars; Calculations for Ssilicon Detector Response to the Pion Beam)

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LOS ALAMOS SCIENTIFIC LABORATORY. LO5 ALAMOS. NEW MEXICO 87545 DATE March 30, 1977 fif'.TO DISTRIBUTION SUBJECT : Pion 1 Calculation Please rwiew the two attached outlines for propored calculations to be done with PION 1 and return with your (1) Dose Perturbations at Interfaces Due to (2) Calculations for Silicon Detector Response to the Pion Beam (CR).

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Dose Perturbations at Interfaces Due t o Pion Stars With conventional radiation using x-rays, gama rays, o r electrons, It is ustl.1 to find relative enhancements or decreases i n dose across the inter - face between dissimilar media. explained by delta - rays and their subsequent scattering s. Pion stars, however initially distribute secondary particles isotropic ally with relatively little delta-ray production. We wish t o determine the possible dose pertur bat ions across bone/musclc Interfaces in a regions of uniform and nonuniform spat181 distribution of pion stars. This i s primarily a.electronic phenomenon Aside from multiple scattering, the location of pion starm is detcrmined by the initial energy spectrum and the mass-stopping-powers of the media through which it passes. This is primarily an electronic phenomenon and to frist order in biological tissues the number of stars per gram ata given range iea constant. The energy distribution from charged star secon d aries is also determined by the mass stopping power of the various media. Since dose 18 the energy deposited in8 volume divided by the mass of the volume, dose per unit path length along an Ionization track is equivalent t o stopping-pwer. Thus, t o first order, dose doer not change across an To second order, the mass-stopping-power does vary from one type of tissue to the next. into tissue than the reverse, yielding an enhanced tissue dose and a depressed bone dose near the interface. Considering that bone and rissue doses would already differ by about 62, the total effect across the interface could b e around 1OZ in physical dose. For example, the ratio of bone t o muscle 1s about 0.94 Such differences can cause more secondaries t o pass from bone Next, it I s noted t h ? tthe excess of energy crossing from bone into tissue will be inthe form of particles near the end of their range and the deficit of energy crossing from tissue into bone is the absence of such partic les wlrh higher than average LET and the depression in bone is due the absence of such particles. physical dose at the interface,there may be a significantly larger difference Thus the energy enhancement i n muscle is expected t o be from parTherefore, i f there is a10%difference in Finally it I s noted that the physical composition differs slightly between bone and mecle. formation for different nuclei scales as 2. Excluding hydrogen the we rage 2's are 7.6 for muscle and 8.3 for bone. This difference ineffective Z is slightly less than the differences between carbon and nitrogen or nitrogen and oxygen. So It would appear that knowing the actual star products from calcium and phosphorous is less important than the differences between t h e much more common elements i n both muscle and bone. For pion stars at rest it may be assumed that star

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Dose Perturbations at Interfaces Due to Pion Stars - 22 f 3For pion stars in flight, the cross sections may be scaled a8 A . Again excluding hydrogen, the average A ' s are 16.6 for bone and lS.3 for muscle. BO that the bone/muscle ratio of inflight stars is about 1.06, which essentially offsets the lower stopping power in bone. region dose differences should be limited differences in primary flux caused by multiple scattering. Thus in the plateau Five calculations are to be considered and are defined in more detail bone/muaclr interface parallel to a 8t8ndard beam. ca8e in a uniform phantom for comparision with experiment and PIPLAN calculations m d to aid interpetation of the interface calculation. For the parallel interface there are three regions of interest: (1) bone stopping region next t o muscle plateau region, (2) muscle stopping region past bone stopping region and (3) adjacent plateau regions. Calculations with multiple scattering turned on and off will allow separation of secondary and primary particle interface effects. Each has regions of high resolution. Three are concerned with a The first 10 a base The remaining NO calculations deal with interfaces in a uniform, extended stopping region (large momentum spread). Again there is a bnse case for comparison with experiment PIPLAN calculation, and PION 1 interface calculation. The bone in this cast has interfaces both normal and parallel to the beam, edged onto the central axis, and centered in the muscle stopping The geometries defined below should be compatible with present PTOR 1 capabilities. The main problem is one of statistics In small volume elements when the looked for effects are on the order of 10% perturbations. But these calculations would appear to bc the best available and should serve as reliable guides in generally predicting interface efftcts. expense is warrented, AB such, the computer 1. Bsse Case - Unspread Momentum Dose distribution in muscle (TE fluid to be used in experiment), using 78.8 WcV i s 18.8 cm In water, 19.0 cm In muscle. Pion range at Rectangular dose accumulation gird, 1 cm resolution for -6?Xf+6 ern, -6:y<+ 6cm. 052524 cat; embedded In this gird are 3 high resolution bands

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Dost Perturbations at Interfaces L to Pion Stars - 3Same geometry and dose accumulation grid as in Bone Case 1 above, except replace muscle with bone for X40. Range of 78.8 MeVn- In Bone is Assume physical density of 1.85 gm/cm3 or range of-11 cm. A. Run with multiple scattering turned off. B. Run with all interactions enabled. 3. Base Case - Spread Momentum Doee distribution in muscle using beam tape for run 428. to give uniform stopping distribution from 9.0 to 15.0 cm, but with rangestraggling included. In muscle 67.8 MeV piona have a range of 15 cm and 19.4 MeV pions have a range o f . 9 cm. - 6 f y t + 6 , 0 t Z b 2 0 cm; embedded in this grid is a high resolution volume 4. Interface Normal to Beam Same beam and dose grid as in Case 3 above, except replace muscle with bone for volume with XLO and Z ~ 1 2cm.

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Calculations € o r S'ilicon Detector Response .t othe Pion Beam X t would be helpful to have a theot et ical guide t o the response of 8 6mr;Tl detector of silicon,tothe be8m. The detector is small compared t o the nize of the field. It's aflat cylinder 2 ann i n diameter and SO thick. In p8rticulu the dose produced by the pions, t h e protons and would be c8l cula tcd to see if a separation can be made. The c8l cula tiw ahould be made for tune 23 and range eh if t cr It io convenient in this work to define the function F(E) which 58 .the energy per unit lOg8TitkmiC interval in energy deporited i n the Let N(E) be the number of pulses in the detector of energy The function F(E) is obtained from t h e experimental d8ta.- Different thickness of detector8 .are being used to separate the The calc ul8tion8 could be a guide 88 t o when the s spa ration We can go down to 7 m thickness easily md2 For obt8lning the LET spectra the dirt ri but ioa of path lengths for the protons and th dS is necessary.

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Exptr ~ mtn tall yt here are three dist i & u ish able groups of particles ; the first group consists of pions, muons and electrons,the second group consistv of the singly charged particles, and the third group consists of the multiply chbrged particles. FOT biology the proton component can probably be lumped with t h e pion component. but to elucidate the physics these components should be An a final goal w e need t o aim for an approximate enalycris of the The final dose calculations as sb-energy spectra of these particles. tai ned from an ion chamber depends on these spectra thru the W valves. For therapeutic guide we also need the function s,"From such a function, one can read off the.dose i n various finite intervals of LET.