NASA/TP–2009-215953

Pion Total Cross Section in Nucleon - Nucleon

Collisions

John W. Norbury

Langley Research Center, Hampton, Virginia

December 2009
NASA STI Program . . . in Profile

Since its founding, NASA has been dedicated to

the advancement of aeronautics and space science.

The NASA scientific and technical information (STI)

program plays a key part in helping NASA maintain

this important role.

The NASA STI program operates under the

auspices of the Agency Chief Information Officer. It

collects, organizes, provides for archiving, and

disseminates NASA’s STI. The NASA STI program

provides access to the NASA Aeronautics and Space

Database and its public interface, the NASA Technical

Report Server, thus providing one of the largest

collections of aeronautical and space science STI in

the world. Results are published in both non-NASA

channels and by NASA in the NASA STI Report

Series, which includes the following report types:

TECHNICAL PUBLICATION. Reports of

completed research or a major significant phase

of research that present the results of NASA

programs and include extensive data or

theoretical analysis. Includes compilations of

significant scientific and technical data and

information deemed to be of continuing

reference value. NASA counterpart of peerreviewed formal professional papers, but having

less stringent limitations on manuscript length

and extent of graphic presentations.

TECHNICAL MEMORANDUM. Scientific

and technical findings that are preliminary or of

specialized interest, e.g., quick release reports,

working papers, and bibliographies that contain

minimal annotation. Does not contain extensive

analysis.

• CONTRACTOR REPORT. Scientific and

technical findings by NASA-sponsored

contractors and grantees.

• CONFERENCE PUBLICATION. Collected

papers from scientific and technical

conferences, symposia, seminars, or other

meetings sponsored or co-sponsored by NASA.

• SPECIAL PUBLICATION. Scientific,

technical, or historical information from NASA

programs, projects, and missions, often

concerned with subjects having substantial

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientific and

technical material pertinent to NASA’s mission.

Specialized services also include creating custom

thesauri, building customized databases, and

organizing and publishing research results.

For more information about the NASA STI

program, see the following:

• Access the NASA STI program home page at

http://www.sti.nasa.gov

• E-mail your question via the Internet to

help@sti.nasa.gov

• Fax your question to the NASA STI Help Desk

at 443-757-5803

• Phone the NASA STI Help Desk at

443-757-5802

• Write to:

NASA STI Help Desk

NASA Center for AeroSpace Information

7115 Standard Drive

Hanover, MD 21076-1320
NASA/TP–2009-215953

Pion Total Cross Section in Nucleon-Nucleon

Collisions

John W. Norbury

Langley Research Center, Hampton, Virginia

National Aeronautics and

Space Administration

Langley Research Center

Hampton, Virginia 23681-2199

December 2009
Acknowledgments

I wish to thank Dr. Ryan Norman for gathering additional experimental data.

Available from:

NASA Center for AeroSpace Information

7115 Standard Drive

Hanover, MD 21076-1320

443-757-5802
Contents

1 Introduction 1

2 Proton -proton reactions 2

3 Neutron -neutron reactions 3

4 Neutron -proton reactions 4

5 Conclusions 4

v
Nomenclature

Throughout this paper, natural units are used, where  ̄h - c - 1.

Elab Total energy of the projectile in the lab frame, in units of MeV or GeV.

Tlab Kinetic energy of the projectile in the lab frame, in units of MeV or GeV.

plab Momentum of the projectile in the lab frame, in units of MeV or GeV.

M Projectile mass, in units of MeV or GeV.

√

s Center of momentum total energy, in units of MeV or GeV.

p Symbol for proton.

n Symbol for neutron.

d Symbol for deuteron (bound state of neutron and proton).

X Generic symbol for unspecified particles.

7r Symbol for pion.

7r+ Symbol for positively charged pion.

7r− Symbol for negatively charged pion.

7r± Symbol for charged pions.

7r0 Symbol for neutral pion.

a Pion production total cross section, in units of mb.

app→*7rX Total cross section for the reaction p + p —* 7r + X.

vi
List of Figures

1 Parameterized inclusive cross sections for pion production in proton - proton

collisions given by equations (1) - (3). The green dotted line is app_»r+X. The red

solid line is app_»r0X. The blue long dashed line is app_»r-X. The black dotted

curve is calculated from 12 (app_»r+X + app_»r-X

). Cross sections are set to zero

for energies below threshold.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Same as Figure 1, except only the low energy region is shown. . . . . . . . . . . 6

3 Same as Figure 1, except only the low energy region is shown and the vertical

scale is logarithmic.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4 Same as Figure 1, except a higher energy region is shown and the vertical and

horizontal scales are logarithmic. Nonphysical behavior sets in at about 500 GeV. 7

5 Log - log plot of the 7r+ total inclusive cross section parameterization (green, solid

line) of equation (1) versus experimental data (triangle symbols) of references

[3, 4, 6, 7, 9, 14] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

6 Same as figure 5, except for use of linear axes. . . . . . . . . . . . . . . . . . . . 8

7 Log - log plot of total inclusive cross section parameterization (blue, solid line) of

equation (2) for the reaction p + p -* 7r- + X versus experimental data (triangle

symbols) of references [3, 4, 7, 9, 14, ?]. Also shown is the cross section data

(solid squares) from Abdivaliev [10], for the reaction n + p -* 7r- + X, compared

to the parameterization (blue, dashed line) of equation (9) . . . . . . . . . . . . . 9

8 Same as Figure 7, except for use of linear axes and n+p reaction is not shown. . 9

9 Log - log plot of total inclusive cross section parameterization (red, solid line) of

equation (3) for the reaction p + p -* 7r0 + X versus experimental data (triangle

symbols) of references [3, 5, 8, 11, 14, 15, 17, 18, 19, 20]. . . . . . . . . . . . . . 10

10 Same as Figure 9, except for use of linear axes, and the p + n -* 7r0 + X data

point of Azimov [8] (solid square at 300 GeV) is now shown. The data points for

p + p -* 7r0 + X of Whitmore [3] (solid triangle at 303 GeV) and Azimov [8] (open

diamond at 300 GeV) have been slightly shifted horizontally so that they do not

overlap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

List of Tables

1 Reaction thresholds. Tlab is the kinetic energy threshold, plab is the momentum

threshold, and Vfs is the center of momentum total energy at threshold. The mass

of the deuteron is 1876.125 MeV. Particle C is the produced particle of interest

and is the first particle listed on the right hand side of each reaction. X are the

remaining particles. Note that cross sections for n + p are the same as for p + n. 11

2 Cross section data for pion production in proton - neutron reactions. . . . . . . 12

3 Cross section data for 7r± production in proton - proton reactions. . . . . . . . . 13

4 Cross section data for 7r0 production in proton - proton reactions.. . . . . . . . . 14

vii
Abstract

Total cross section parameterizations for neutral and charged pion production in

nucleon - nucleon collisions are compared to experimental data over the projectile

momentum range from threshold to 300 GeV. Both proton - proton and proton -

neutron reactions are considered. Overall excellent agreement between parameterizations and experiment is found, except for notable disagreements near threshold.

In addition, the hypothesis that the neutral pion production cross section can be

obtained from the average charged pion cross section is checked. The theoretical

formulas presented in the paper obey this hypothesis for projectile momenta below

500 GeV. The results presented provide a test of engineering tools used to calculate

the pion component of space radiation.

1 Introduction

Hadron production in nuclear and nucleon collisions can be a significant source of space radiation, especially for planetary atmospheres. The most important hadron is the pion, because

it has the lowest threshold for production. While total production cross sections are not used

in transport equations, it is nevertheless worthwhile to understand them thoroughly because

integrated differential cross sections must always equal total cross sections. The aim of this research is to obtain an excellent parameterization of pion production cross sections from nucleon

- nucleon and nucleus - nucleus collisions. A good understanding of the energy dependence and

nuclear mass dependence will then provide a further test of the accuracy of differential cross

sections, when they are integrated. In addition, total cross sections may be used to generate

differential cross sections. The method for generating these differential cross sections is outlined

in reference [1]. The idea is to multiply the total cross section by functions that give the shape

of the differential cross section. One then multiplies by a normalizing factor, so that the result equals the total cross section when integrated. This method is useful if the shape of the

differential cross section is accurately known, because the integrated differential cross section

is guaranteed to give the correct total cross section. The total cross section parameterizations

developed previously [2], were compared to only nine experimental data points all above 10

GeV. The cosmic ray spectrum peaks near the pion threshold at 280 MeV, and therefore it is

worthwhile to compare to more low energy data. The present work compares parameterizations

to over thirty experimental data points ranging from threshold to about 300 GeV. Finally, an

approximation that one often sees in the literature is that the neutral pion cross section can be

obtained from the average of the charged pion cross sections. This hypothesis will tested.

1
2 Proton -proton reactions

The total inclusive cross section for pion production in proton - proton collisions has been

parameterized as [2]

!−1

app—»r+X =0.00717 + 0.0652log Tlab + 0.162 (1) Tlab Tlab

pp - 0.00456 + 0.00856 + 0.5757 -

1

2 ->7r -x - ( ) Tlab Tlab

!−1

app—»r0X =0.007+0.

1 log Tlab + 0

2

3

(3) Tlab Tlab

where Tlab is the kinetic energy of the projectile, which is given in units of GeV to give a in

units of mb. These cross sections are plotted in Figures 1 - 4 as a function of plab, which is the

momentum of the projectile. These quantities are related via

Tlab = Elab — m =

q

p2lab + m2 — m , (4)

where m is the projectile mass. In equations (1) - (3), the cross sections are set equal to zero

for energies below threshold. The thresholds are shown in Table 1.

An interesting aspect of pion production is that the following relation holds.

1

app—»r0X ^ 2 (app—»r-X + app—»r+X) , (5)

which is shown as the black dotted curve in Figures 1 - 4, which closely follows the red solid

curve (cross section for 7r0), and shows that equation (5) works very well for all energies. Figure

4 shows that nonphysical behavior sets in at about 500 GeV, where the curves intersect and

cross over each other. This phenomenon is nonphysical because the 7r- cross section should

not be larger than the 7r+ cross section. The parameterizations should not be used above this

energy.

The parameterizations in equations (1) - (3) are compared to experimental data in Figures 5

- 10, which are shown as both linear and logarithmic plots. The reason for this is seen clearly, for

example, in Figures 5 and 6. Figure 6 seems to show overall very good agreement between the

parameterization and experiment. However, when plotted on a logarithmic scale, as in Figure

5 one can now see poor agreement for the data point at 1.38 GeV, which was not apparent on

the linear plot.

In reference [2], the parameterizations of equations (1) - (3) were compared only to three data

points from Whitmore [3] at plab = 12, 19 and 24 GeV. In the present work, paramterizations

are also compared to the Whitmore data at 69, 102, 205 and 303 GeV, and data from other

authors [4, 5]. More importantly, paramterizations are also compared to some other low energy

data [6, 7, 8, 9, 10]. Comparison is made to the data point at plab = 954 MeV, corresponding

to Tlab = 400 MeV, of Abd El-Samad et al. [11]. The cross section for the reaction pp -* pp7r0

is 0.1 mb. Even though this is an exclusive final state, the exclusive cross section is equal to the

2
inclusive cross section because the energy is below the two pion threshold. See Table 1. The

complete set of experimental data is listed in Tables 2, 3, and 4. Note that Booth et al. [4] only

report the cross section for 7r+ plus 7r- production, defined as Q,,f at plab = 8.8 GeV. Therefore,

the individual 7r+ and 7r- cross sections listed in Table 3 represent the experimental cross section

of Booth et al. [4], but with the theoretically calculated individual pion cross section subtracted

off using equations 1 and 2, i.e.

Q,,

+ (Table 3) - Q,f (Booth) - Q,- (equation 2), (6)

Q,,

- (Table 3) - Q,f (Booth) - Q,+ (equation 1). (7)

Figures 5 and 6 show the comparison of equation (1) to the experimental data. The

p + p -* 7r+ + X threshold occurs at Tlab = 289 MeV, or plab = 791 MeV, because this is the lowest energy reaction for which a 7r+ particle is produced. See Table 1. Comparison between the

parameterization and experiment is excellent for high energies up to 300 GeV and down to 3.67

GeV. However, at the lower energy of 1.38 GeV, which is closer to threshold, there is significant

disagreement between the parameterization and experiment, with with the experimentally obtained cross sections being much larger than those obtained from the parameterization. Norbury

et al. [12] have recently shown that cross sections near threshold are important because they

are enhanced due to larger cosmic ray flux. Figures 7 and 8 show the comparison of equation

(2) to the experimental data. The p + p -* 7r- + X threshold occurs at Tlab = 600 MeV, or

plab = 1219 MeV (see Table 1). These thresholds are much larger than for 7r+ production and

explains why the 7r+ cross section is always larger than the 7r- cross section, as shown in Figure

1. The 7r- cross section should never be larger than the 7r+ cross section because more energy is

required to produce 7r- particles. Comparison between the parameterization and experiment is

excellent for high energies up to 300 GeV and down to 3.67 GeV. However, at the lower energy

of 1.38 GeV, there is significant disagreement between the parameterization and experiment,

this time with the experimentally obtained cross sections being much smaller than those obtained from the parameterization. Note that now the momentum of 1.38 GeV is very close to

the 7r- threshold at 1.219 GeV, and is considered a near threshold cross section [12]. Figures

9 and 10 show the comparison of equation (3) to the experimental data. The p + p -* 7re + X

threshold occurs at Tlab = 280 MeV, or plab = 777 MeV. See Table 1. Comparison between the

parameterization and experiment is excellent, but there is significant disagreement at the high

momentum of 300 GeV. The near threshold cross section parameterization is significantly larger

than experiment.

3 Neutron -neutron reactions

Examining the reactions shown in Table 1, reveals that the neutron - neutron (nn) cross section

for pion production should be the same as for the proton - proton (pp) reaction, if one ignores

isospin. While Coulomb effects may be important at low energies, the reactions should be equal

at higher energies. Therefore,

Qnn—>,X ^ Qpp—>,X (8)

for all pion species. Unfortunately, there is no data to test this.

3
4 Neutron -proton reactions

Consideration of the reactions shown in Table 1, plus consideration of multiple pion reactions

[13] suggests that, at low energy, the neutron - proton (np) cross section might be a simple

multiple of the pp cross section. The reaction, n + p —* 7r— + X, has been studied by Abdivaliev

[10] and the data are shown in Figure 7, compared to the following simple parameterization

(dashed line) of the np cross section,

Unp→»r-X = 2. 5 Upp→»r-X , (9)

where Upp→»r-X is given in equation (2). The np experimental cross sections for other pion

species (7r+ and 7r0 ) are not available, and parameterizations cannot be developed.

At higher energies, one may expect pion production cross sections for all pp, np and nn

reactions to become equal given the proliferation of multiple pion production. This expectation

seems to be verified by the two data points of Azimov [8] at 300 GeV shown in Figure 10. The

open triangle is for the reaction p + p —* 7r0 + X, and the solid square is for p + n —* 7r0 + X. The

experimental cross section in this high energy region, near 300 GeV, seems to obey the relation

Upn→»r0X R^ Upp→»r0X . (10)

Finally, one would expect

Unp→»rX = Upn—»rX (11)

to hold at all energies for all pion species.

5 Conclusions

Total cross section parameterizations for neutral and charged pion production in nucleon -

nucleon collisions have been compared to an extensive set of experimental data over the projectile

momentum range from threshold to 300 GeV. For 7r± production, the disagreement between the

parameterization and experiment near threshold at plab = 1.38 GeV needs to be resolved. This

disagreement is not obvious in the linear plots, but shows up clearly in the logarithmic plots.

For 7r0 production, the disagreement between the parameterization and experiment at plab =

300 GeV needs to be resolved. There is a need for more experimental measurements of pn cross

sections for all pion species at low and high energy. In spite of these disagreements, there is

excellent overall agreement between parameterizations and experiment. Above the energy region

near threshold, the parameterizations provide accurate cross section predictions. The results can

be used to validate engineering tools used to calculate the pion component of space radiation.

4
References

[1] J. W. Norbury and A. Adamczyk, Nucl. Inst. Meth. Phys. Res. B 254, 177 (2007).

[2] S. R. Blattnig, S. R. Swaminathan, A. T. Kruger, M. Ngom, and J. W. Norbury, Phys.

Rev. D 62, 094030 (2000).

[3] J. Whitmore, Physics Reports 10, 273 (1974). See Table 12 for data.

[4] C. N. Booth et al., Phys. Rev. D 27, 2018 (1983).

[5] R. D. Kass, W. Ko, R. L. Lander, W. Michael, D. E. Pellett, P. M. Yager, R. Ely, G. Gidal,

and P. Hanson, Phys. Rev. D 20, 605 (1979).

[6] J. F. Crawford et al., Phys. Rev. C 22, 1184 (1980).

[7] A. C. Melissinos, T. Yamanouchi, G. G. Fazio, S. J. Lindenbaum, and L. C. L. Yuan, Phys.

Rev. 128 2373 (1962). See Table III for data.

[8] See data listing for the reaction p + p —* π

°

+ X, for author named Azimov at

http://durpdg.dur.ac.uk/HEPDATA/

[9] D. R. F. Cochran et al., Phys. Rev. D 6, 3085 (1972). See Table XII for data.

[10] A. Abdivaliev, K. Besliu, S. Gruia, A. P. Ierusalimov, F. Kotorobai, V. I. Moroz, A. V.

Nikitin, D. Pantea, V. N. Pechenov, and Yu. A. Troian, JINR-P1-82-507 (1982). Data

available at http://durpdg.dur.ac.uk/HEPDATA/

[11] S. Abd El-Samad et al., Eur. Phys. J. A 30, 443 (2006).

[12] J. W. Norbury, L. W. Townsend, and R. B. Norman Journal of Physics G 34, 115 (2007).

[13] J. W. Norbury and L. W. Townsend, Nucl. Inst. Meth. Phys. Res. B 254, 187 (2007).

[14] V. Blobel et al., Nucl. Phys. B 69, 454 (1974).

[15] K. Jaeger, J. Campbell, G. Charlton, D. Swanson, C. Fu, H. A. Rubin, R. G. Glasser, D.

Koetke, and J. Whitmore, Phys. Rev. D 11, 1756 (1975).

[16] H. Blumenfeld et al., Phys. Lett. B 45, 525 (1973).

[17] M. Boratav et al., Nucl. Phys. B 111, 529 (1976).

[18] J. W. Chapman, J. Cooper, N. Green, B. P. Roe, A. A. Seidl, J. C. Vander Velde, C. M.

Bromberg, D. Cohen, T. Ferbel, and P. Slattery, Phys. Lett. B 47, 465 (1973).

[19] K. Jaeger, D. Colley, L. Hyman, and J. Rest, Phys. Rev. D 11, 2405 (1975).

[20] F. T. Dao, D. Gordon, J. Lach, E. Malamud, J. Schivell, T. Meyer, R. Poster, P. E. Schlein,

and W. E. Slater, Phys. Rev. Lett. 30, 1151 (1973).

5
80

60

s (mb)

40

20

p + p -> Tr + X

100

0 20 40 60 80 100

plab (GeV)

Figure 1: Parameterized inclusive cross sections for pion production in proton - proton

collisions given by equations (1) - (3). The green dotted line is Upp-„r+X. The red solid line

is Upp-„r0X. The blue long dashed line is app-„r-X. The black dotted curve is calculated

from 000-pion.nb 1

2 (Upp-„r+X + Upp-,7r-X). Cross sections are set to zero for energies below threshold.

p + p -> Tr + X

25

20

15

s (mb )

10

5

1 2 3 4 5

plab (GeV)

Figure 2: Same as Figure 1, except only the low energy region is shown.

6
cv (mb) 3

2

1.5

1

2((

15(

1((

7(

s (mb) 5(

3(

2(

15

15

10

7

5

p + p -> p + X

1 1.5 2 2.5 3

p lab (GeV)

Figure 3: Same as Figure 1, except only the low energy region is shown and the vertical

scale is logarithmic.

1( 5( 1(( 5(( 1((( 5(((

plab (GeV)

Figure 4: Same as Figure 1, except a higher energy region is shown and the vertical and

horizontal scales are logarithmic. Nonphysical behavior sets in at about 500 GeV.

7
s(mb)

140

120

100

80

60

40

20

0

p + p ->Tr++ X

100

50

s(mb)

10

5

1

1 5 10 50 100

plab (GeV)

Figure 5: Log - log plot of the 7r+ total inclusive cross section parameterization (green,

solid line) of equation (1) versus experimental data (triangle symbols) of references [3, 4,

6, 7, 9, 14].

p + p ->p++ X

0 50 100 150 200 250 300

plab (GeV)

Figure 6: Same as figure 5, except for use of linear axes.

8
s(mb)

140

120

100

80

60

40

20

0

(p,n) + p -> p

- + X

100

10

s(mb) 1

0.1

0.01 ^I I I I I 1 5 10 50 100

plab (GeV)

Figure 7: Log - log plot of total inclusive cross section parameterization (blue, solid line) of

equation (2) for the reaction p + p —* 7r- + X versus experimental data (triangle symbols)

of references [3, 4, 7, 9, 14, ?] . Also shown is the cross section data (solid squares) from

Abdivaliev [10], for the reaction n + p —* 7r- + X, compared to the parameterization (blue,

dashed line) of equation (9).

p + p ->p-+ X

0 50 100 150 200 250 300

plab (GeV)

Figure 8: Same as Figure 7, except for use of linear axes and n+p reaction is not shown.

9
n + n ->p0 + X

100

s(mb)

10

0.1

plab (GeV)

Figure 9: Log - log plot of total inclusive cross section parameterization (red, solid line) of

equation (3) for the reaction p + p —* 70 + X versus experimental data (triangle symbols)

of references [3, 5, 8, 11, 14, 15, 17, 18, 19, 20].

p + (p,n) -> Tr0

 + X

140

120

100

s(mb) 80

60

40

20

0

0 50 100 150 200 250 300

plab (GeV)

Figure 10: Same as Figure 9, except for use of linear axes, and the p + n —* 70 + X

data point of Azimov [8] (solid square at 300 GeV) is now shown. The data points for

p + p —* 70 +X of Whitmore [3] (solid triangle at 303 GeV) and Azimov [8] (open diamond

at 300 GeV) have been slightly shifted horizontally so that they do not overlap.

10
Table 1: Reaction thresholds. Tlab is the kinetic energy threshold, plab is the momentum

threshold, and 

N 

J is the center of momentum total energy at threshold. The mass of

the deuteron is 1876.125 MeV. Particle C is the produced particle of interest and is the

first particle listed on the right hand side of each reaction. X are the remaining particles.

Note that cross sections for n + p are the same as for p + n.

A+ B -* C+ X Tlab plab

N J

(MeV) (MeV) (MeV)

p+p -* 7r

0 +p+p 279.7 776.6 2011.5

7r0 + 7r0 + p + p 578.7 1192.1 2146.5

7r+ + p + n 292.3 796.2 2017.4

7r+ + d 288.6 790.5 2015.7

7r- + 7r+ + p + p 599.8 1218.7 2155.7

n+n -* 7r

0 +n+n 279.7 777.0 2014.1

7r+ + 7r- + n + n 599.8 1219.3 2158.3

7r- + p + n 286.7 788.0 2017.4

7r- + d 283.0 782.3 2015.7

p+n -* 7r

0 +p+n 279.5 776.2 2012.8

7r0 + d 275.8 770.5 2011.1

7r+ + n + n 292.1 795.9 2018.7

7r- + p + p 286.5 787.3 2016.1

11
Table 2: Cross section data for pion production in proton - neutron reactions.

Reaction Tlab

(GeV)

plab

(GeV)

NFS

(GeV)

Q

(mb)

Reference

p + n π

0

+ X 299.1 300 23.8 136 + 10 [8]

n + p π- + X 0.62 1.25 2.17 1.45 + 0.06 [10]

1.03 1.73 2.34 4.1 + 0.1 [10]

1.48 2.23 2.51 8.7 + 0.3 [10]

3.00 3.83 3.03 16.44 + 0.51 [10]

4.25 5.1 3.39 21.0 + 0.53 [10]

12
Table 3: Cross section data for 7r± production in proton - proton reactions.

Reaction Tlab

(GeV)

plab

(GeV)

NFS

(GeV)

Q

(mb)

Reference

p + p -* 7r+ +X 0.59 1.2 2.2 9.7 + 1.2 [6]

0.73 1.38 2.21 13.5 + 0.73 [9]

2.85 3.67 2.98 26.1 + 5.0 [7]

7.91 8.8 4.3 39.9 + 0.6 [4]

11.1 12 4.9 43.2 + 0.9 [3, 14]

18.1 19 6.1 47.5 + 1.0 [3]

23.1 24 6.8 56.8 + 0.9 [3, 14]

68.1 69 11.5 81.5 + 8.2 [3]

101.1 102 13.9 91.8 + 9.2 [3]

204.1 205 19.7 108 + 11 [3]

302.1 303 23.9 125 + 13 [3]

p + p -* 7r− +X 0.73 1.38 2.2 0.03 + 0.01 [9]

2.85 3.67 2.98 6.0 + 1.2 [7]

7.91 8.8 4.3 19.1 + 0.6 [4]

11.1 12 4.9 21.3 + 0.4 [3, 14]

18.1 19 6.1 30 + 0.6 [3, ?]

23.1 24 6.8 33.8 + 0.6 [3, 14]

68.1 69 11.5 62.7 + 1.0 [3]

101.1 102 13.9 66.9 + 1.3 [3]

204.1 205 19.7 86 + 2 [3]

302.1 303 23.9 99.5 + 3.0 [3]

13
Table 4: Cross section data for 7r° production in proton - proton reactions.

Reaction Tlab

(GeV)

plab

(GeV)

NFS

(GeV)

Q

(mb)

Reference

p + p 7r° + X 0.4 0.954 2.07 0.1 + 0.007 [11]

11.1 12 4.9 31.5 + 2.6 [3, 14, 15]

18.1 19 6.1 41.6 + 3.5 [3]

23.1 24 6.8 53.5 + 3.1 [3, 14]

68.1 69 11.5 81.1 + 4 [3, 16, 17]

101.1 102 13.9 85 + 8 [3, 18]

204.1 205 19.7 107.3 + 6.8 [3, 19]

299.1 300 23.8 130 + 5 [8]

302.1 303 23.9 127 + 12 [3, 20]

399.1 400 27.4 142.3 + 6.2 [5]

14
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing

data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or

any other aspect of this collection of information, including suggestions for reducing this burden, to Department of Defense, Washington Headquarters Services, Directorate

for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that

notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently

valid OMB control number.

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE 3. DATES COVERED (From - To)

01-12-2009 Technical Publication

4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER

Pion Total Cross Section in Nucleon - Nucleon Collisions

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S) 5d. PROJECT NUMBER

Norbury, John W.

5e. TASK NUMBER

5f. WORK UNIT NUMBER

651549.02.07.01

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION

REPORT NUMBER

NASA Langley Research Center

Hampton, VA 23681-0001 L-19597

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITOR'S ACRONYM(S)

National Aeronautics and Space Administration NASA

Washington, DC 20546-0001

11. SPONSORING/MONITORING

REPORT NUMBER

NASA/TP-2009-215953

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited

Subject Category 93 Availability: NASA CASI (443) 757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

Total cross section parameterizations for neutral and charged pion production in nucleon - nucleon collisions are compared to

experimental data over the projectile momentum range from threshold to 300 GeV. Both proton - proton and proton - neutron

reactions are considered. Overall excellent agreement between parameterizations and experiment is found, except for notable

disagreements near threshold. In addition, the hypothesis that the neutral pion production cross section can be obtained from the

average charged pion cross section is checked. The theoretical formulas presented in the paper obey this hypothesis for projectile

momenta below 500 GeV. The results presented provide a test of engineering tools used to calculate the pion component of space

radiation.

15. SUBJECT TERMS

Total cross section; Pion production; Space radiation

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18. NUMBER 19a. NAME OF RESPONSIBLE PERSON

ABSTRACT

PA

OF

PAGES Help Desk (email: p il hle sti.nasa. ov ( p@ g ) a. REPORT b. ABSTRACT c. THIS PAGE

19b. TELEPHONE NUMBER (Include area code) UU U U U 22 (443) 757-5802

Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18