The wave-function we have used is called uncorrelated because of the fact that the probabilityįor finding a particle at position and another one at is uncorrelated, i.e. ![]() The procedure is repeated until the ground state and the corresponding energy at step do not deviate appreciably from those in the previous step. SOlving the Schrödinger equation for this potential one finds a new ground state, which is in turn used to build a new potential. To solve this kind of problem, we start searching for a solution with some trial wave-function, which is used for constructing the potential. This is a self-consistent problem: is the solution to the Schrödinger equation, but the Hamiltonian deppends on itself. However, the Hamiltonian deppends on the wave-function we are looking for. We now have a single-particle Hamiltonian for the wave-function of a single electron. The third term on the left hand side can be recognized as the Coulomb energy of particle 1 in the electric field generated by the charge density of particle 2. Related technical methods are under development at NIST in the United States and at PTB in Germany, and the authors' research team has also undertaken related research.Where several integrals we have removed the constant terms that do not deppend on by absorving them into. ![]() Since the refractive index of a gas can be precisely measured by optical methods, this becomes a metrology method for optically determining the density (pressure) of gases. The polarizability of helium atoms can be accurately calculated and the refractive index of helium gas can be derived. The reason for this deviation has not been explained, and the solution of this problem will provide an important reference to solve the 'puzzle of proton radius.' At present, there is still a significant deviation between the measured results of the difference between the nuclear radius of helium-3 and helium-4. Spectroscopy of the helium atom has been applied to determine the radius of helium nuclei. In the 1960s, theorists discovered that the fine-structure split (23P0-23P2) of the 23P energy level of. In addition, precision measurement of helium also has a broad impact to various important studies. Helium atom precision measurements and calculations have a history of nearly a century. ![]() This will be an extremely strict test of QED. On the one hand, it may be developed through theoretical development, and on the other hand, it may be explored through precision measurements of other helium-like ions. Recent experimental progresses obtained in several groups worldwide are introduced, including the 2S-2P transition frequency of He-4 and the 23P0-23P2 fine structure interval determined by the authors' research group, which are the most accurate results to date.Īt present, the accuracy of calculated results of helium is limited by the very complicated QED correction of the 8th order of α. After 50 years of hard work, theorists have develoed different approaches to calculate the QED correction of helium to the 7th power series of α.Įxperimental precision measurements of helium atoms have been carried out in many international research institutions. Such a measurement of α from precision spectroscopy of helium, compared with values determined from totally different methods, presents a perfect test of the consistency of physics. It covers almost all physical systems from microscopic particles to macroscopic solids, and is currently the most accurate theory in physics. QED is the basic theory describing the quantum properties of electromagnetic interactions. In the 1960s, theorists discovered that the fine-structure split (23P0-23P2) of the 23P energy level of helium is the best atomic system for measuring the fine structure constant α (approximately 1/137), which is the key parameter in the Quantum Electrodynamics (QED) theory. The supersonic helium atom beam, with a very narrow energy spread of less than 1 meV, can be created through free-jet expansion of helium at a pressure of 2 × 10 7 Pa into a low-vacuum chamber (10 2 Pa at the steady state during beam operation) through a nozzle with small diameter of 510 m. When it comes to net charge, the balance between electrons and protons will determine whether. Helium atom precision measurements and calculations have a history of nearly a century. The net charge on the helium atom is zero. The fine structure constant determined by different methods.
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