Difference between revisions of "Energy Loss (d2n)"
From Hall A Wiki
(→Yellow Cover) |
(→3He Glass Cell Characteristics) |
||
| (14 intermediate revisions by the same user not shown) | |||
| Line 67: | Line 67: | ||
|} | |} | ||
| − | + | = 3He Glass Cell Characteristics = | |
* Material: Aluminosilicate (GE180) | * Material: Aluminosilicate (GE180) | ||
** <math>\rho</math>: 2.76 <math>\textrm{g}/\textrm{cm}^3</math> | ** <math>\rho</math>: 2.76 <math>\textrm{g}/\textrm{cm}^3</math> | ||
** <math>X_0</math>: 19.4246 <math>\textrm{g}/\textrm{cm}^2</math> | ** <math>X_0</math>: 19.4246 <math>\textrm{g}/\textrm{cm}^2</math> | ||
| − | ** <math> | + | ** <math>Z_{\textrm{eff}} = 19.56</math> |
| − | ** <math> | + | ** <math>A_{\textrm{eff}} = 40.51</math> <math>\textrm{g/mol}</math> |
| − | + | ** Composition by weight: | |
| − | Composition by weight: | + | |
{| border="1" | {| border="1" | ||
| − | | '''Material''' || '''Composition by Weight (%)''' || '''<math> | + | | '''Material''' || '''Composition by Weight (%)''' || '''<math>Z_{\textrm{eff}}</math>''' || '''<math>Z/A</math>''' |
|- | |- | ||
| − | |SiO<math>_2</math> || 60.3 || | + | |SiO<math>_2</math> || 60.3 || 11.56 || 0.4993 |
|- | |- | ||
| − | |BaO || 18.2 || | + | |BaO || 18.2 || 53.52 || 0.4174 |
|- | |- | ||
| − | |Al<math>_2</math>O<math>_3</math> || 14.3 || | + | |Al<math>_2</math>O<math>_3</math> || 14.3 || 11.14 || 0.4904 |
|- | |- | ||
| − | |CaO || 6.5 || | + | |CaO || 6.5 || 17.99 || 0.4993 |
|- | |- | ||
| − | |SrO || 0.25 || | + | |SrO || 0.25 || 35.64 || 0.4439 |
|- | |- | ||
| − | | Totals/Averages || 99.55 || | + | | Totals/Weighted Averages || 99.55 || 19.56 || 0.4829 |
|} | |} | ||
| + | |||
| + | * <math>Z_{\textrm{eff}}</math> is calculated as: <math>Z_{\textrm{eff}} = \left(\sum_i f_i Z_i^{2.94}\right)^{1/2.94}</math>, where <math>f_i</math> is the fraction of electrons associated with each element in the compound. | ||
| + | * <math>A_{\textrm{eff}}</math> is calculated as: <math>A_{\textrm{eff}} = \frac{Z_{\textrm{eff}}}{Z/A}</math> | ||
| + | |||
| + | = Useful Links = | ||
| + | |||
| + | * [http://pdg.lbl.gov/2010/AtomicNuclearProperties/index.html Atomic-Nuclear Properties of Materials] | ||
Latest revision as of 15:46, 24 January 2011
We can divide the energy loss problem into two parts: energy loss for incoming electrons (before the primary scattering interaction), and energy loss for outgoing electrons (after the primary scattering interaction). The tables below, with reference to Chiranjib's dissertation, show the materials in the path of each set of electrons, plus a mean energy loss calculation for a nominal scattering angle of <math>45^{\circ}</math>.
Please note that the actual energy loss curve follows a Landau distribution, and the most likely energy loss value is NOT the same as the mean energy loss reported below.
Chiranjib Dutta's dissertation (especially the appendices) is a good resource.
Contents
Mean Energy Loss for Incoming Electrons
All thicknesses taken from Chiranjib's dissertation.
| Material | <math>X_0</math> (cm) | Thickness (cm) | Thickness (<math>X_0</math>) | Mean Energy Loss <math>(\langle E_f \rangle - E_i)/E_i</math> |
| Beam pipe window (Be) | 35.28 | 0.0254 | 0.000719 | 0.00072 |
| He-4 in target enclosure | 528107.5 | 22.86 | 0.000043 | 0.000043 |
| Target entrance window (glass) | 7.038 | 0.01 | 0.00142 | 0.001420 |
| 19.8 cm (half cell length) of He-3 | 43423 | 19.8 | 0.000456 | 0.000456 |
Mean Energy Loss for Outgoing Electrons
- For the He-3 and target side wall, starred quantities (thickness and mean energy loss) assume a scattering angle of 45 degrees.
- The He-4 thickness and mean energy loss assumes that the target enclosure is spherically symmetric around the interaction point. In actuality this depends on the vertex position.
| Material | <math>X_0</math> (cm) | Thickness (cm) | Thickness (<math>X_0</math>) | Mean Energy Loss <math>(\langle E_f \rangle - E_i)/E_i</math> |
| He-3 in cell | 43423 | 1.34* | 0.000031* | 0.000031* |
| Side wall of target cell (glass) | 7.038 | 0.156* | 0.022165* | 0.021922* |
| He-4 in target enclosure | 528107.5 | 79.05 | 0.000150 | 0.000150 |
| Air (distance is for LHRS) | 30423 | 51.23 | 0.001684 | 0.001682 |
| Kapton entry window (LHRS) | 28.6 | 0.0254 | 0.000888 | 0.000887 |
Yellow Cover
Since the composition and thickness of the yellow cover on the target enclosure is not quite known, the table below gives sample values, assuming a thickness of 35 mils = 0.0889 cm and spherical symmetry about the interaction point, for several different types of plastics listed in the PDG table of Atomic and Nuclear Products and Materials.
| Material | <math>X_0</math> (cm) | Thickness (cm) | Thickness (<math>X_0</math>) | Mean Energy Loss <math>(\langle E_f \rangle - E_i)/E_i</math> |
| Nylon | 35.525 | 0.0889 | 0.00250 | 0.00250 |
| Polycarbonate | 34.583 | 0.0889 | 0.00257 | 0.00257 |
| Polyethylene | 50.303 | 0.0889 | 0.00177 | 0.00176 |
| Mylar | 28.536 | 0.0889 | 0.00312 | 0.00311 |
| Kapton | 28.577 | 0.0889 | 0.00311 | 0.00311 |
| Acrylic | 34.076 | 0.0889 | 0.00261 | 0.00260 |
| Polypropylene | 49.744 | 0.0889 | 0.00179 | 0.00178 |
| Polystyrene | 41.311 | 0.0889 | 0.00215 | 0.00215 |
| Teflon | 15.836 | 0.0889 | 0.00561 | 0.00560 |
| Polyvinyltoluene | 42.621 | 0.0889 | 0.00208 | 0.00208 |
3He Glass Cell Characteristics
- Material: Aluminosilicate (GE180)
- <math>\rho</math>: 2.76 <math>\textrm{g}/\textrm{cm}^3</math>
- <math>X_0</math>: 19.4246 <math>\textrm{g}/\textrm{cm}^2</math>
- <math>Z_{\textrm{eff}} = 19.56</math>
- <math>A_{\textrm{eff}} = 40.51</math> <math>\textrm{g/mol}</math>
- Composition by weight:
| Material | Composition by Weight (%) | <math>Z_{\textrm{eff}}</math> | <math>Z/A</math> |
| SiO<math>_2</math> | 60.3 | 11.56 | 0.4993 |
| BaO | 18.2 | 53.52 | 0.4174 |
| Al<math>_2</math>O<math>_3</math> | 14.3 | 11.14 | 0.4904 |
| CaO | 6.5 | 17.99 | 0.4993 |
| SrO | 0.25 | 35.64 | 0.4439 |
| Totals/Weighted Averages | 99.55 | 19.56 | 0.4829 |
- <math>Z_{\textrm{eff}}</math> is calculated as: <math>Z_{\textrm{eff}} = \left(\sum_i f_i Z_i^{2.94}\right)^{1/2.94}</math>, where <math>f_i</math> is the fraction of electrons associated with each element in the compound.
- <math>A_{\textrm{eff}}</math> is calculated as: <math>A_{\textrm{eff}} = \frac{Z_{\textrm{eff}}}{Z/A}</math>
