PhD Proposal Tamar - Revision history

Didbtama: /* Calculating the Error in \frac{\Delta d_v}{d_v} */

2012-12-08T05:06:28Z

Calculating the Error in \frac{\Delta d_v}{d_v}

Oborn: /* Calculating the Error in \frac{\Delta d_v}{d_v} */

2010-07-07T22:58:50Z

Calculating the Error in \frac{\Delta d_v}{d_v}

Oborn: /* Calculating the Error in \frac{\Delta d_v}{d_v} */

2010-07-07T22:36:31Z

Calculating the Error in \frac{\Delta d_v}{d_v}

Oborn: /* Calculating the Error in \frac{\Delta d_v}{d_v} */

2010-07-05T22:28:20Z

Calculating the Error in \frac{\Delta d_v}{d_v}

Oborn: /* Calculating the Error in \frac{\Delta d_v}{d_v} */

2010-04-20T20:34:13Z

Calculating the Error in \frac{\Delta d_v}{d_v}

Oborn: /* Calculating the Error in \frac{\Delta d_v}{d_v} */

2010-02-22T18:51:20Z

Calculating the Error in \frac{\Delta d_v}{d_v}

Oborn: /* Target */

2010-02-13T00:07:38Z

Target

Oborn: /* Target */

2010-02-13T00:07:14Z

Target

Oborn: /* Target */

2010-02-13T00:05:53Z

Target

Oborn: /* Introduction */

2010-02-11T21:14:30Z

Introduction

← Older revision		Revision as of 05:06, 8 December 2012
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	[[File:TheQuarkModel_2.pdf]]		[[File:TheQuarkModel_2.pdf]]
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		+	[http://wiki.iac.isu.edu/index.php/User_talk:Didbtama Go Back]

← Older revision		Revision as of 22:58, 7 July 2010
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	:: <math>+ Z (\partial N_1 - \partial N_2 - \partial N_3 + \partial N_4 - 4\partial N_5 + 4\partial N_6 + 4\partial N_7 - 4\partial N_8) \}^2</math>		:: <math>+ Z (\partial N_1 - \partial N_2 - \partial N_3 + \partial N_4 - 4\partial N_5 + 4\partial N_6 + 4\partial N_7 - 4\partial N_8) \}^2</math>

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		+	[http://search.digikey.com/scripts/DkSearch/dksus.dll?Detail&name=609-1778-ND]

	[[File:TamarProposal.pdf]]		[[File:TamarProposal.pdf]]

← Older revision		Revision as of 22:36, 7 July 2010
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	[[File:TamarProposalP_1.pdf]]		[[File:TamarProposalP_1.pdf]]

−	[[File:~~TheQuarkModel_1~~.pdf]]	+	[[File:TheQuarkModel_2.pdf]]

← Older revision		Revision as of 22:28, 5 July 2010
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	[[File:TamarProposalP_1.pdf]]		[[File:TamarProposalP_1.pdf]]
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		+	[[File:TheQuarkModel_1.pdf]]

← Older revision		Revision as of 20:34, 20 April 2010
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	[[File:TamarProposal.pdf]]		[[File:TamarProposal.pdf]]
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		+	[[File:TamarProposalP_1.pdf]]

← Older revision		Revision as of 18:51, 22 February 2010
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−	<math>\partial F(d)= \{ \frac{\partial F}{\partial N_1} \times \partial N_1 + \frac{\partial F}{\partial N_2} \times \partial N_2 + \frac{\partial F}{\partial N_3} \times \partial N_3 + \frac{\partial F}{\partial N_4} \times \partial N_4 + \frac{\partial F}{\partial N_5} \times \partial N_5 + \frac{\partial F}{\partial N_6} \times \partial N_6 + \frac{\partial F}{\partial N_7} \times \partial N_7 + \frac{\partial F}{\partial N_8} \times \partial N_8 \}^2 = </math> <br>	+	<math>\partial F(d)= \{ \frac{\partial}{\partial N_1} \times \partial N_1 + \frac{\partial}{\partial N_2} \times \partial N_2 + \frac{\partial}{\partial N_3} \times \partial N_3 + \frac{\partial}{\partial N_4} \times \partial N_4 + \frac{\partial}{\partial N_5} \times \partial N_5 + \frac{\partial}{\partial N_6} \times \partial N_6 + \frac{\partial}{\partial N_7} \times \partial N_7 + \frac{\partial}{\partial N_8} \times \partial N_8 \}^2 F </math> <br>

	:: <math>= \frac{1}{Z^4} \{ Y ( - \partial N_1 - \partial N_2 + \partial N_3 + \partial N_4 + 4\partial N_5 + 4\partial N_6 - 4\partial N_7 - 4\partial N_8) + </math><br>		:: <math>= \frac{1}{Z^4} \{ Y ( - \partial N_1 - \partial N_2 + \partial N_3 + \partial N_4 + 4\partial N_5 + 4\partial N_6 - 4\partial N_7 - 4\partial N_8) + </math><br>

@@ Line 279: / Line 279: @@
 ;Target Materials
-The EG1 experiment at Jefferson Lab used five different targets to  measure the polarized structure functions of the nucleon and perform background corrections <ref name="Polarized target for the CLAS detector"> Keith, C. D., et al. (2003). A Polarized target for the CLAS detector. NIM, A501, 327-339.</ref>. The main target materials for the experiment used frozen ammonia, <math>15NH_3</math>, for the polarized protons and deuterated ammonia, <math>15ND_3</math> for the polarized deuterons.  A target ladder, placed 50 cm upstream of the standard CLAS target position, was used to position the desired target. The target ladder was designed and built in collaboration with the Italian Istituto di Fisica Nucleare, TJNAF, Oxford instruments and the University of Virginia. The solid targets NH3 and ND3 were polarized using the method of Dynamic Nuclear Polarization(DNP) achieving the average polarization of target to beam product for 5.7 GeV run <math>P_b \times P_t = (0.51 \pm 0.01)</math> and <math>P_b \times P_t = (0.19 \pm 0.03)</math> respectively <ref name="Dharmawardane2006"> Dharmawardane, K.V., et al., (The CLAS Collaboration). (2006). Measurement of the x and <math>Q^2</math>-Dependence of the Spin Asymmetry <math>A_1</math> on the Nucleon. Phys. Lett., B641, 11.</ref><br>. Three other targets, C12, liquid He-4 and N15 were used to remove the Nitrogen and Helium background from NH3 and ND3 target data. Helium is used to cool the ammonia targets. Dynamic Nuclear Polatization is a process when the polarization of free electrons is transferred to the protons in the target.<ref name="LEADER"> Leader, E. (2001). Spin in Particle Physics. Cambridge, UK: Cambridge University Press.</ref>In DNP the target is doped with paramagnetic impurities by chemical doping or by irradiating the target in electron beam.  For low temperatures and high magnetic field, such as the ratio of a magnetic field to temperature is <math>\approx 5 Tesla/K</math>, the free electron polarization is approximately 100%, on the other hand the protons inside the target are unpolarized. Under a microwave field with the frequency close to the electron spin resonance induce the transitions which flip the spin of the electron and nearby proton in the target. The relaxation time of the electron is <math>10^{-3} s</math>, whereas the relaxation time of the proton in the target is <math>10^3 s</math>. Due to such a big difference of the relaxation time of the proton and electron, the flipped electron spin rapidly returns to its thermal equilibrium state from where it induces the proton spin-flip again. As a result, the spin polarization is transferred to the protons after some time. <br>
+The EG1 experiment at Jefferson Lab used five different targets to  measure the polarized structure functions of the nucleon and perform background corrections <ref name="Polarized target for the CLAS detector"> Keith, C. D., et al. (2003). A Polarized target for the CLAS detector. NIM, A501, 327-339.</ref>. The main target materials for the experiment used frozen ammonia, <math>15NH_3</math>, for the polarized protons and deuterated ammonia, <math>15ND_3</math> for the polarized deuterons.  A target ladder, placed 50 cm upstream of the standard CLAS target position, was used to position the desired target. The target ladder was designed and built in collaboration with the Italian Istituto di Fisica Nucleare, TJNAF, Oxford instruments and the University of Virginia. The solid targets NH3 and ND3 were polarized using the method of Dynamic Nuclear Polarization(DNP) achieving the average polarization of target to beam product for 5.7 GeV run <math>P_b \times P_t = (0.51 \pm 0.01)</math> and <math>P_b \times P_t = (0.19 \pm 0.03)</math> respectively <ref name="Dharmawardane2006"> Dharmawardane, K.V., et al., (The CLAS Collaboration). (2006). Measurement of the x and <math>Q^2</math>-Dependence of the Spin Asymmetry <math>A_1</math> on the Nucleon. Phys. Lett., B641, 11.</ref>. Three other targets, C12, liquid He-4 and N15 were used to remove the Nitrogen and Helium background from NH3 and ND3 target data. Helium is used to cool the ammonia targets. Dynamic Nuclear Polatization is a process when the polarization of free electrons is transferred to the protons in the target.<ref name="LEADER"> Leader, E. (2001). Spin in Particle Physics. Cambridge, UK: Cambridge University Press.</ref>In DNP the target is doped with paramagnetic impurities by chemical doping or by irradiating the target in electron beam.  For low temperatures and high magnetic field, such as the ratio of a magnetic field to temperature is <math>\approx 5 Tesla/K</math>, the free electron polarization is approximately 100%, on the other hand the protons inside the target are unpolarized. Under a microwave field with the frequency close to the electron spin resonance induce the transitions which flip the spin of the electron and nearby proton in the target. The relaxation time of the electron is <math>10^{-3} s</math>, whereas the relaxation time of the proton in the target is <math>10^3 s</math>. Due to such a big difference of the relaxation time of the proton and electron, the flipped electron spin rapidly returns to its thermal equilibrium state from where it induces the proton spin-flip again. As a result, the spin polarization is transferred to the protons after some time. <br>
 Ammonia targets were selected because of their ability to produce high polarization and they are less effected by beam radiation. The damage caused by this radiation can be repaired by annealing. The target is warmed up to liquid nitrogen temperature for annealing.  In addition, the ammonia target has a high ratio of free nucleons  (~3/18) approximately 16.7 % for <math>15NH_3</math> and 28.6 % for <math>15ND_3</math>. One disadvantage of choosing ammonia is the polarization background caused by 15N(spin - 1/2), or 14N(spin - 1), which was accounted for by taking data using a solid N-15 target.<ref name="Polarized target for the CLAS detector"> Keith, C. D., et al. (2003). A Polarized target for the CLAS detector. NIM, A501, 327-339.</ref> <ref name="Chen">S. Chen, Ph.D Thesis, The Florida State University (2006)</ref>

@@ Line 8: / Line 8: @@
 ==Introduction==
-Electron scattering has been used for more than 40 years to measure the structure of a nucleon, a neutron or a proton.  The early experiments at the Stanford Linear Accelerator Center (SLAC) showed that a nucleon(hadron) was really composed of constituents called quarks. The constituent quark model describes a baryon as a combination of three quarks and mesons as a quark-antiquark bound state. According to the quark model, two of the three quarks in a proton are labeled as having a flavor ``up" and the remaining quark a flavor ``down". The two up quarks have fractional  charge <math>+\frac{2}{3}e</math>  while the down quark has a charge <math>-\frac{1}{2}e</math>  All quarks have spin <math>\frac{1}{2}</math>. In the quark model each quark carries one third of the nucleon mass.
+Electron scattering has been used for more than 40 years to measure the structure of a nucleon, a neutron or a proton.  The early experiments at the Stanford Linear Accelerator Center (SLAC) showed that a nucleon(hadron) was really composed of constituents called quarks. The constituent quark model describes a baryon as a combination of three quarks and mesons as a quark-antiquark bound state. According to the quark model, two of the three quarks in a proton are labeled as having a flavor "up" and the remaining quark a flavor "down". The two up quarks have fractional  charge <math>+\frac{2}{3}e</math>  while the down quark has a charge <math>-\frac{1}{2}e</math>  All quarks have spin <math>\frac{1}{2}</math>. In the quark model each quark carries one third of the nucleon mass.
 While elastic scattering measures the ground state properties of a nucleon, inelastic scattering experiments are used to probe a nucleon's excited states. The experiments at the SLAC used high energy electrons scattered by nucleons. The mediator between the target nucleon and coulomb scattering of an electron is the virtual photon. The four-momentum, Q,  of the virtual photon serves as a measure of the resolution of the scattering and may be formulated as: