Hyperfine splitting of the dressed hydrogen atom ground state in non-relativistic QED

We consider a spin-1/2 electron and a spin-1/2 nucleus interacting with the quantized electromagnetic field in the standard model of non-relativistic QED. For a fixed total momentum sufficiently small, we study the multiplicity of the ground state of the reduced Hamiltonian. We prove that the coupling between the spins of the charged particles and the electromagnetic field splits the degeneracy of the ground state.Comment: 22 page

Hyperfine splitting in non-relativistic QED: uniqueness of the dressed hydrogen atom ground state

We consider a free hydrogen atom composed of a spin-1/2 nucleus and a spin-1/2 electron in the standard model of non-relativistic QED. We study the Pauli-Fierz Hamiltonian associated with this system at a fixed total momentum. For small enough values of the fine-structure constant, we prove that the ground state is unique. This result reflects the hyperfine structure of the hydrogen atom ground state.Comment: 22 pages, 3 figure

Kagera Regional and District Projections

This report presents population projections for the period 2003 to 2025 for the Kagera Region and its districts. The projections were made using a Cohort Component Method (Spectrum System), whereby three components responsible for population change, namely: mortality, fertility and migration were projected separately as well as HIV/AIDS prevalence. The projected components were then applied to 2002 midyear base population in order to come up with the desired projections from 2003 to 2025. The report gives mortality, fertility, migration and HIV/AIDS assumptions, which depicts Kagera’s demographic and socio-economic future trends. The results include estimated population by sex in single years and five-year age groups as well as some demographic indicators. Population growth for the period 2003 to 2025 shows an increase in growth rates. The projections show that population growth rate will increase from 3.1 percent in 2003 (with a population of 1,982,612) to 3.7 percent in 2025 (with a population of 4,511,927). Sex Ratio at birth is projected to increase from 96 male births per 100 females in 2003 to 99 male births per 100 females in 2025. Mortality estimates show that Infant Mortality Rate (IMR) is expected to decline for both sexes from 117 deaths per 1,000 live births in 2003 to 72 deaths per 1,000 live births in 2025. Under Five Mortality Rate (U5MR) for both sexes will also decline from 195 deaths per 1,000 live births in 2003 to 113 deaths per 1,000 live births in the year 2025. The mortality projected estimates further show that the life expectancy at birth for females is higher compared to that of males, which is expected. Life expectancy at birth for Kagera will increase from 48 years in 2003 to 55 years in 2025 for both sexes. For male population, life expectancy at birth will increase from 46 years in year 2003 to 54 years in 2025, while for female population the life expectancy at birth will increase from 49 years in 2003 to 56 years in 2025

Iringa Regional and District Projections.

This report presents population projections for the period 2003 to 2025 for Iringa Region and its districts. The projections were made using a Cohort Component Method (Spectrum System), whereby three components responsible for population change, namely: mortality, fertility and migration were projected separately as well as HIV/AIDS prevalence. The projected components were then applied to 2002 midyear base population in order to come up with the desired projections from 2003 to 2025. The report gives mortality, fertility, migration and HIV/AIDS assumptions, and shows Iringa’s demographic and socio-economic future trends. The results include estimated population by sex in single years and five-year age groups as well as some demographic indicators. Population growth for the period 2003 to 2025 shows a decrease in growth rates. The projections show that population growth rate will decrease from 1.6 percent in 2003 (with a population of 1,520,891) to 0.4 percent in 2025 (with a population of 2,019,217). Sex Ratio at birth is projected to increase from 90 male births per 100 females in 2003 to 99 male births per 100 females in 2025. Mortality estimates show that Infant Mortality Rate (IMR) is expected to decline for both sexes from 127 deaths per 1,000 live births in 2003 to 78 deaths per 1,000 live births in 2025. Under Five Mortality Rate (U5MR) for both sexes will also decline from 207 deaths per 1,000 live births in 2003 to 122 deaths per 1,000 live births in the year 2025. The mortality projected estimates further show that the life expectancy at birth for both males and females stands at 45 years in 2003. Life expectancy at birth for Iringa will decline from 45 years in 2003 to 44 years in 2025 for both sexes. For male population, life expectancy at birth will remain at the same level of 45 years in year 2003 and year 2025, while for female population the life expectancy at birth will decline from 45 years in 2003 to 43 years in 2025. On fertility, TFR will decline from 4.9 children per woman in 2003 to 2.6 children per woman in 2025.\u

Dar es Salaam Regional and District Projections.

This report presents population projections for the period 2003 to 2025 for Dar es Salaam Region. The projections were made using a Cohort Component Method (Spectrum System), whereby three components responsible for population change, namely: mortality, fertility and migration were projected separately as well as HIV/AIDS prevalence. The projected components were then applied to 2002 midyear base population in order to come up with the desired projections from 2003 to 2025. The report gives mortality, fertility, migration and HIV/AIDS assumptions, and shows Dar es Salaam’s demographic and socio-economic future trends. The results include estimated population by sex in single years and five-year age groups as well as some demographic indicators. Population growth for the period 2003 to 2025 shows a decrease in growth rates. The projections show that population growth rate will decrease from 1.99 percent in 2003 (with a population of 2,535,594) to 0.27 percent in 2025 (with a population of 3,055,456). Sex Ratio at birth is projected to increase slightly from 102 male per 100 females in 2003 to 103 male per 100 females in 2025. Mortality estimates show that Infant Mortality Rate (IMR) is expected to decline for both sexes from 80 deaths per 1,000 live births in 2003 to 49 deaths per 1,000 live births in 2025. Under Five Mortality Rate (U5MR) for both sexes will also decline from 122 deaths per 1,000 live births in 2003 to 71 deaths per 1,000 live births in the year 2025. As expected, the mortality projected estimates further show that the life expectancy at birth for females is higher compared to that of males. Life expectancy at birth for Dar es Salaam will decline from 55 years in 2003 to 52 years in 2025 for both sexes. For male population, life expectancy at birth will almost remain at 53 years for the whole period. For female population, the life expectancy at birth will decline from 57 years in 2003 to 52 years in 2025. On fertility, TFR will decline from 2.7 children per woman in 2003 to about 2 children per woman in 2025.\u

Lindi Regional and District Projections

\ud This report presents population projections for the period 2003 to 2025 for Lindi Region and its districts. The projections were made using a Cohort Component Method (Spectrum System), whereby three components responsible for population change, namely: mortality, fertility and migration were projected separately as well as HIV/AIDS prevalence. The projected components were then applied to 2002 midyear base population in order to come up with the desired projections from 2003 to 2025. The report gives mortality, fertility, migration and HIV/AIDS assumptions, and shows Lindi’s demographic and socio-economic future trends. The results include estimated population by sex in single years and five-year age groups as well as some demographic indicators. Population growth for the period 2003 to 2025 shows fluctuations. The projections show that\ud population growth rate will increase from 1.4 percent in 2003 (with a population of 801,189) to 1.6 percent in 2025 (with a population of 1,209,623). Sex Ratio at birth is projected to increase from 93 males births per 100 females in 2003 to 97 males births per 100 females in 2025. Mortality estimates show that Infant Mortality Rate (IMR) is expected to decline for both sexes from 116 deaths per 1,000 live births in 2003 to 53 deaths per 1,000 live births in 2025. Under Five Mortality Rate (U5MR) for both sexes will also decline from 194 deaths per 1,000 live births in 2003 to 80 deaths per 1,000 live births in the year 2025. The mortality projected estimates further show that the life expectancy at birth for females is higher compared to that of males. Life expectancy at birth for Lindi will increase from 48 years in 2003 to 60 years in 2025 for both sexes. For male population, life expectancy at birth will increase from 47 years in year 2003 to 59 years in 2025, while for female population the life expectancy at birth will increase from 49 years in 2003 to 61 years in 2025. On fertility, TFR will decline from 4.4 children per woman in 2003 to 3.4 children per woman in 2025.\u

Singida Regional and District Projections

\ud This report presents population projections for the period 2003 to 2025 for Singida Region and its districts. The projections were made using a Cohort Component Method (Spectrum System), whereby three components responsible for population change, namely: mortality, fertility and\ud migration were projected separately as well as HIV/AIDS prevalence. The projected components were then applied to 2002 midyear base population in order to come up with the desired projections from 2003 to 2025. The report gives mortality, fertility, migration and HIV/AIDS assumptions, and shows Singida’s demographic and socio-economic future trends. The results include estimated population by sex in single years and five-year age groups as well as some demographic indicators. The results show that population growth for the period 2003 to 2025 shows a decrease in growth rates. The projections show that population growth rate will decrease from 2.4 percent in 2003 (with a population of 1,118,874) to 1.5 percent in 2025 (with a population of 1,897,726). Sex Ratio at birth is projected to increase from 95 males per 100 females in 2003 to 100 males per 100 females in 2025. Mortality estimates show that Infant Mortality Rate (IMR) is expected to decline for both sexes from 84 deaths per 1,000 live births in 2003 to 43 deaths per 1,000 live births in 2025. Under Five Mortality Rate (U5MR) for both sexes will also decline from 135 deaths per 1,000 live births in 2003 to 62 deaths per 1,000 live births in the year 2025. The mortality projected estimates further show that the life expectancy at birth for females is higher compared to that of males as expected. Life expectancy at birth for Singida will increase from 55 years in 2003 to 63 years in 2025 for both sexes. For male population, life expectancy at birth will increase from 56 years in year 2003 to 63 years in 2025, while for female population, the life expectancy at birth will increase from 54 years in 2003 to 63 years in 2025. On fertility, TFR will decline from 6.0 children per woman in 2003 to 3.0 children per woman in 2025.\u

Mtwara Regional and District Projections.

\ud This report presents population projections for the period 2003 to 2025 for Mtwara region and its districts. The projections were made using a Cohort Component Method (Spectrum System), whereby three components responsible for population change, namely: mortality, fertility and\ud migration were projected separately as well as HIV/AIDS prevalence. The projected components were then applied to 2002 midyear base population in order to come up with the desired projections from 2003 to 2025. The report gives mortality, fertility, migration and HIV/AIDS assumptions, and shows Mtwara’s demographic and socio-economic future trends. The results include estimated population by sex in single years and five-year age groups as well as some demographic indicators. Population growth for the period 2003 to 2025 shows an increase from 1.8 percent in 2003 (with a population of 1,145,655) to 2.0 percent in 2009 (with a population of 1,297,751) and will decrease gradually to 1.8 in 2025 (with a population of 1,724,679). Sex Ratio at birth is projected to increase from 90 male births per 100 females in 2003 to 97 male births per 100 females in 2025. Mortality estimates show that Infant Mortality Rate (IMR) is expected to decline for both sexes from 143 deaths per 1,000 live births in 2003 to 84 deaths per 1,000 live births in 2025. Under Five Mortality Rate (U5MR) for both sexes will also decline from 238 deaths per 1,000 live births in 2003 to 134 deaths per 1,000 live births in the year 2025. Life expectancy at birth for Mtwara will increase from 43 years in 2003 to 48 years in 2025 for both sexes. For male population, life expectancy at birth will increase from 43 years in year 2003 to 48 years in 2025, while for female population the life expectancy at birth will increase from 42 years in 2003 to 48 years in 2025. On fertility, TFR will decline from 4.9 children per woman in 2003 to 4.6 children per woman in 2025.\u

Manyara Regional and District Projections

This report presents population projections for the period 2003 to 2025 for the Manyara Region and its districts. The projections were made using the Cohort Component Method (Spectrum System), whereby three components responsible for population change, namely: mortality, fertility and migration are projected separately as well as HIV/AIDS prevalence. The projected components are then applied to 2002 midyear base population in order to come up with the desired projections from 2003 to 2025. The report gives mortality, fertility, migration and HIV/AIDS assumptions, which depicts Manyara’s demographic and socio-economic future trends. The results include estimated population by sex in single years and five-year age groups as well as some demographic indicators. Population growth for the period 2003 to 2025 shows an increase in growth rates. The projections show that population growth rate will increase from 3.9 percent in 2003 (with a population of 1,075,022) to 4.2 percent in 2025 (with a population of 2,483,873). Sex Ratio at birth is projected to decrease from 105 male births per 100 females in 2003 to 103 male births per 100 females in 2025. Mortality estimates show that Infant Mortality Rate (IMR) is expected to decline for both sexes from 62 deaths per 1,000 live births in 2003 to 31 deaths per 1,000 live births in 2025. Under Five Mortality Rate (U5MR) for both sexes will also decline from 96 deaths per 1,000 live births in 2003 to 42 deaths per 1,000 live births in the year 2025. The mortality projected estimates further show that the life expectancy at birth for females is higher compared to that of males, which is expected. Life expectancy at birth for Manyara will increase from 61 years in 2003 to 68 years in 2025 for both sexes. For male population, life expectancy at birth will increase from 60 years in year 2003 to 66 years in 2025, while for female population the life expectancy at birth will increase from 62 years in 2003 to 69 years in 2025. On fertility, TFR will increase from 6.4 children per woman in 2003 to 6.8 children per woman in 2025

Morogoro Regional and District Projections

\ud This report presents population projections for the period 2003 to 2025 for the Morogoro Region and its districts. The projections were made using a Cohort Component Method (Spectrum System), whereby three components responsible for population change, namely: mortality, fertility and migration were projected separately as well as HIV/AIDS prevalence. The projected components were then applied to 2002 midyear base population in order to come up with the desired projections from 2003 to 2025. The report gives mortality, fertility, migration and HIV/AIDS assumptions, and shows Morogoro’s demographic and socio-economic future trends. The results include estimated population by sex in single years and five-year age groups as well as some demographic indicators. Population growth for the period 2003 to 2025 shows a decrease in growth rates. The projections show that population growth rate will decrease from 2.3 percent in 2003 (with a population of 1,794,815) to 1.7 percent in 2025 (with a population of 2,818,784). Sex Ratio at birth is projected to increase from 99 male births per 100 females in 2003 to 101 male births per 100 females in 2025. Mortality estimates show that Infant Mortality Rate (IMR) is expected to decline for both sexes from 105 deaths per 1,000 live births in 2003 to 63 deaths per 1,000 live births in 2025. Under Five Mortality Rate (U5MR) for both sexes will also decline from 171 deaths per 1,000 live births in 2003 to 98 deaths per 1,000 live births in the year 2025. The mortality projected estimates further show that the life expectancy at birth for males is slightly lower compared to that of females. Life expectancy at birth for Morogoro will increase from 50 years in 2003 to 54 years in 2025 for both sexes. For male population, life expectancy at birth will increase from 50 years in year 2003 to 54 years in 2025, while for female population, the life expectancy at birth will increase from 50 years in 2003 to 55 years in 2025. On fertility, TFR will decline from 5.0 children per woman in 2003 to 3.7 children per woman in 2025.\u